Roboguru

Sederhanakan pecahan berikut. e.

Pertanyaan

Sederhanakan pecahan berikut.

e. begin mathsize 14px style fraction numerator 3 over denominator a squared minus 1 end fraction minus fraction numerator 2 over denominator a plus 1 end fraction end style

Pembahasan Soal:

Diketahui pecahan aljabar begin mathsize 14px style fraction numerator 3 over denominator a squared minus 1 end fraction minus fraction numerator 2 over denominator a plus 1 end fraction end style.

Ingat kembali cara mengurangkan bentuk pecahan biasa:

fraction numerator a over denominator b c end fraction minus d over b equals fraction numerator a minus c d over denominator b c end fraction 

Untuk menyederhanakan pecahan aljabar di atas dengan cara memfaktorkan begin mathsize 14px style a squared minus 1 end style meggunakan begin mathsize 14px style a squared minus b squared equals open parentheses a minus b close parentheses open parentheses a plus b close parentheses end style baru dijumlahkan atau dikurangkan.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 3 over denominator a squared minus 1 end fraction minus fraction numerator 2 over denominator a plus 1 end fraction end cell equals cell fraction numerator 3 over denominator open parentheses a minus 1 close parentheses cross times open parentheses a plus 1 close parentheses end fraction minus fraction numerator 2 over denominator a plus 1 end fraction end cell row blank equals cell fraction numerator 3 minus 2 open parentheses a minus 1 close parentheses over denominator open parentheses a minus 1 close parentheses cross times open parentheses a plus 1 close parentheses end fraction end cell row blank equals cell fraction numerator 3 minus 2 a plus 2 over denominator a squared minus 1 end fraction end cell row blank equals cell fraction numerator 5 minus 2 a over denominator a squared minus 1 end fraction end cell end table end style

Jadi, bentuk sederhana pecahan dari begin mathsize 14px style fraction numerator 3 over denominator a squared minus 1 end fraction minus fraction numerator 2 over denominator a plus 1 end fraction equals fraction numerator 5 minus 2 a over denominator a squared minus 1 end fraction end style.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

S. Nur

Terakhir diupdate 13 September 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

Tapi Roboguru masih mau belajar. Menurut kamu pembahasan kali ini sudah membantu, belum?

Membantu

Kurang Membantu

Apakah pembahasan ini membantu?

Belum menemukan yang kamu cari?

Post pertanyaanmu ke Tanya Jawab, yuk

Mau Bertanya

Pertanyaan yang serupa

Sederhanakanlah! f.

Pembahasan Soal:

Diketahui bentuk aljabar: 

fraction numerator 3 over denominator m plus 2 end fraction plus fraction numerator m minus 5 over denominator m squared minus 4 end fraction minus fraction numerator 4 over denominator m minus 2 end fraction

Ditanya: bentuk sederhana.

Ingat bahwa:

  • x left parenthesis x plus k right parenthesis equals x left parenthesis x right parenthesis plus x left parenthesis k right parenthesis equals x squared plus x k 
  • x over a minus y over b equals fraction numerator b x over denominator a b end fraction minus fraction numerator a y over denominator a b end fraction equals fraction numerator b x minus a y over denominator a b end fraction   
  • open parentheses a squared minus b squared close parentheses equals left parenthesis a plus b right parenthesis left parenthesis a minus b right parenthesis 

Mencari bentuk sederhana dari fraction numerator 3 over denominator m plus 2 end fraction plus fraction numerator m minus 5 over denominator m squared minus 4 end fraction minus fraction numerator 4 over denominator m minus 2 end fraction:

fraction numerator 3 over denominator m plus 2 end fraction plus fraction numerator m minus 5 over denominator m squared minus 4 end fraction minus fraction numerator 4 over denominator m minus 2 end fraction equals fraction numerator 3 over denominator m plus 2 end fraction plus fraction numerator m minus 5 over denominator open parentheses m plus 2 close parentheses open parentheses m minus 2 close parentheses end fraction minus fraction numerator 4 over denominator m minus 2 end fraction equals fraction numerator 3 open parentheses m minus 2 close parentheses over denominator open parentheses m plus 2 close parentheses open parentheses m minus 2 close parentheses end fraction plus fraction numerator m minus 5 over denominator open parentheses m plus 2 close parentheses open parentheses m minus 2 close parentheses end fraction minus fraction numerator 4 open parentheses m plus 2 close parentheses over denominator open parentheses m minus 2 close parentheses open parentheses m plus 2 close parentheses end fraction equals fraction numerator 3 open parentheses m minus 2 close parentheses plus m minus 5 minus 4 open parentheses m plus 2 close parentheses over denominator open parentheses m plus 2 close parentheses open parentheses m minus 2 close parentheses end fraction equals fraction numerator 3 m minus 6 plus m minus 5 minus 4 m minus 8 over denominator open parentheses m plus 2 close parentheses open parentheses m minus 2 close parentheses end fraction equals fraction numerator negative 19 over denominator open parentheses m plus 2 close parentheses open parentheses m minus 2 close parentheses end fraction equals negative fraction numerator 19 over denominator open parentheses m plus 2 close parentheses open parentheses m minus 2 close parentheses end fraction  

Jadi, bentuk sederhana dari fraction numerator 3 over denominator m plus 2 end fraction plus fraction numerator m minus 5 over denominator m squared minus 4 end fraction minus fraction numerator 4 over denominator m minus 2 end fraction adalah negative fraction numerator 19 over denominator open parentheses m plus 2 close parentheses open parentheses m minus 2 close parentheses end fraction.

0

Roboguru

Diketahui persamaan . Hitung nilai  dan !

Pembahasan Soal:

Operasi hitung campuran pada pecahan bentuk aljabar

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator x minus 1 plus begin display style fraction numerator 2 over denominator x plus 2 end fraction end style over denominator x plus 1 minus begin display style fraction numerator 2 over denominator x plus 2 end fraction end style end fraction end cell equals cell fraction numerator x plus m over denominator x plus n end fraction end cell row cell open parentheses x minus 1 plus fraction numerator 2 over denominator x plus 2 end fraction close parentheses divided by open parentheses x plus 1 minus fraction numerator 2 over denominator x plus 2 end fraction close parentheses end cell equals cell fraction numerator x plus m over denominator x plus n end fraction end cell row cell open square brackets fraction numerator open parentheses x plus 2 close parentheses open parentheses x minus 1 close parentheses plus 2 over denominator open parentheses x plus 2 close parentheses end fraction close square brackets divided by open square brackets fraction numerator open parentheses x plus 2 close parentheses open parentheses x plus 1 close parentheses minus 2 over denominator open parentheses x plus 2 close parentheses end fraction close square brackets end cell equals cell fraction numerator x plus m over denominator x plus n end fraction end cell row cell open square brackets fraction numerator down diagonal strike open parentheses x plus 2 close parentheses end strike open parentheses x minus 1 close parentheses plus 2 over denominator up diagonal strike open parentheses x plus 2 close parentheses end strike end fraction close square brackets cross times open square brackets fraction numerator up diagonal strike open parentheses x plus 2 close parentheses end strike over denominator down diagonal strike open parentheses x plus 2 close parentheses end strike open parentheses x plus 1 close parentheses minus 2 end fraction close square brackets end cell equals cell fraction numerator x plus m over denominator x plus n end fraction end cell row cell fraction numerator x minus 1 plus 2 over denominator x plus 1 minus 2 end fraction end cell equals cell fraction numerator x plus m over denominator x plus n end fraction end cell row cell fraction numerator x plus 1 over denominator x minus 1 end fraction end cell equals cell fraction numerator x plus m over denominator x plus n end fraction end cell end table 

Menentukan nilai m dan n

table attributes columnalign right center left columnspacing 0px end attributes row cell x plus 1 end cell equals cell x plus m end cell row cell x minus x plus 1 end cell equals m row 1 equals m row cell x minus 1 end cell equals cell x plus n end cell row cell x minus x minus 1 end cell equals n row cell negative 1 end cell equals n end table 

Jadi, nilai  m equals 1 comma space n equals negative 1.

0

Roboguru

Bentuk sederhana dari  adalah ...

Pembahasan Soal:

Untuk mencari bentuk sederhana dari fraction numerator 2 over denominator x plus 2 end fraction minus fraction numerator 3 over denominator x plus 3 end fraction, sama kan dulu penyebutnya

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 2 over denominator x plus 2 end fraction minus fraction numerator 3 over denominator x plus 3 end fraction end cell equals cell fraction numerator 2 left parenthesis x plus 3 right parenthesis over denominator x plus 2 end fraction minus fraction numerator 3 left parenthesis x plus 2 right parenthesis over denominator x plus 3 end fraction end cell row blank equals cell fraction numerator 2 x plus 6 over denominator open parentheses x plus 2 close parentheses open parentheses x plus 3 close parentheses end fraction minus fraction numerator 3 x plus 6 over denominator open parentheses x plus 2 close parentheses open parentheses x plus 3 close parentheses end fraction end cell row blank equals cell fraction numerator 2 x plus 6 minus 3 x plus 6 over denominator open parentheses x plus 2 close parentheses open parentheses x plus 3 close parentheses end fraction end cell row blank equals cell fraction numerator 2 x minus 3 x plus 6 plus 6 over denominator open parentheses x plus 2 close parentheses open parentheses x plus 3 close parentheses end fraction end cell row blank equals cell fraction numerator negative x plus 12 over denominator open parentheses x plus 2 close parentheses open parentheses x plus 3 close parentheses end fraction end cell end table

 

Jadi, bentuk sederhana dari fraction numerator 2 over denominator x plus 2 end fraction minus fraction numerator 3 over denominator x plus 3 end fraction adalah fraction numerator negative x plus 12 over denominator open parentheses x plus 2 close parentheses open parentheses x plus 3 close parentheses end fraction.


Oleh karena itu, jawaban yang benar adalah C.

0

Roboguru

Tentukan hasil operasi hitung bentuk aljabar berikut! c.

Pembahasan Soal:

Pada operasi penjumlahan pecahan aljabar dengan penyebut berbeda, samakan dahulu penyebutnya kemudian sederhanakan hasilnya.

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator a plus 5 over denominator 2 a end fraction minus fraction numerator 2 a minus 1 over denominator 4 a end fraction plus fraction numerator 3 a minus 4 over denominator 6 a end fraction end cell equals cell fraction numerator 6 open parentheses a plus 5 close parentheses minus 3 open parentheses 2 a minus 1 close parentheses plus 2 open parentheses 3 a minus 4 close parentheses over denominator 12 a end fraction end cell row blank equals cell fraction numerator 6 a plus 30 minus 6 a plus 3 plus 6 a minus 8 over denominator 12 a end fraction end cell row blank equals cell fraction numerator 6 a plus 25 over denominator 12 a end fraction end cell end table

Jadi, hasil operasi hitung dari table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator a plus 5 over denominator 2 a end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 2 a minus 1 over denominator 4 a end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 3 a minus 4 over denominator 6 a end fraction end cell end table adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 6 a plus 25 over denominator 12 a end fraction end cell end table.

 

0

Roboguru

Pembahasan Soal:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 3 plus x over denominator 4 y end fraction minus fraction numerator 2 minus 5 x over denominator 2 y end fraction end cell equals cell fraction numerator 3 plus x over denominator 4 y end fraction minus fraction numerator 4 minus 10 x over denominator 4 y end fraction end cell row blank equals cell fraction numerator 3 plus x minus 4 plus 10 x over denominator 4 y end fraction end cell row blank equals cell fraction numerator 11 x minus 1 over denominator 4 y end fraction end cell end table end style

0

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

Tapi Roboguru masih mau belajar. Menurut kamu pembahasan kali ini sudah membantu, belum?

Membantu

Kurang Membantu

Apakah pembahasan ini membantu?

Belum menemukan yang kamu cari?

Post pertanyaanmu ke Tanya Jawab, yuk

Mau Bertanya

RUANGGURU HQ

Jl. Dr. Saharjo No.161, Manggarai Selatan, Tebet, Kota Jakarta Selatan, Daerah Khusus Ibukota Jakarta 12860

Coba GRATIS Aplikasi Ruangguru

Produk Ruangguru

Produk Lainnya

Hubungi Kami

Ikuti Kami

©2021 Ruangguru. All Rights Reserved