Sederhanakanlah! b. x2−4x−45x2−9x​

Pertanyaan

Sederhanakanlah!

b. fraction numerator x squared minus 9 x over denominator x squared minus 4 x minus 45 end fraction 

S. Yoga

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

bentuk sederhana dari fraction numerator x squared minus 9 x over denominator x squared minus 4 x minus 45 end fraction adalah fraction numerator x over denominator x plus 5 end fraction.

Pembahasan

Diketahui bentuk aljabar: 

fraction numerator x squared minus 9 x over denominator x squared minus 4 x minus 45 end fraction

Ditanya: bentuk sederhana.

Ingat bahwa pemfaktoran 

  • 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 
  • table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis x plus p right parenthesis left parenthesis x plus q right parenthesis end cell equals cell x left parenthesis x right parenthesis plus x left parenthesis q right parenthesis plus p left parenthesis x right parenthesis plus p left parenthesis q right parenthesis end cell row blank equals cell x squared plus left parenthesis p plus q right parenthesis x plus p q end cell end table  

Mencari bentuk sederhana dengan pemfaktoran dari fraction numerator x squared minus 9 x over denominator x squared minus 4 x minus 45 end fraction:

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator x squared minus 9 x over denominator x squared minus 4 x minus 45 end fraction end cell equals cell fraction numerator x open parentheses x minus 9 close parentheses over denominator x squared minus 4 x minus 45 end fraction end cell row blank equals cell fraction numerator x open parentheses x minus 9 close parentheses over denominator open parentheses x squared plus 5 x close parentheses plus open parentheses negative 9 x minus 45 close parentheses end fraction end cell row blank equals cell fraction numerator x open parentheses x minus 9 close parentheses over denominator x open parentheses x plus 5 close parentheses minus 9 open parentheses x plus 5 close parentheses end fraction end cell row blank equals cell fraction numerator x open parentheses x minus 9 close parentheses over denominator open parentheses x plus 5 close parentheses open parentheses x minus 9 close parentheses end fraction end cell row blank equals cell fraction numerator x over denominator x plus 5 end fraction end cell end table 

Jadi, bentuk sederhana dari fraction numerator x squared minus 9 x over denominator x squared minus 4 x minus 45 end fraction adalah fraction numerator x over denominator x plus 5 end fraction.

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