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Diketahui  tentukan nilai  !

Pertanyaan

Diketahui fraction numerator 5 x squared plus 6 x plus 8 over denominator 4 x minus x cubed end fraction equals A over x plus fraction numerator B over denominator x plus 2 end fraction minus fraction numerator C over denominator x minus 2 end fraction tentukan nilai A comma space B comma space dan space C !

Pembahasan Soal:

Berdasarkan soal diketahui bahwa fraction numerator 5 x squared plus 6 x plus 8 over denominator 4 x minus x cubed end fraction equals A over x plus fraction numerator B over denominator x plus 2 end fraction minus fraction numerator C over denominator x minus 2 end fraction, dengan menyamakan penyebut pada ruas kanan, diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell A over x plus fraction numerator B over denominator x plus 2 end fraction minus fraction numerator C over denominator x minus 2 end fraction end cell equals cell fraction numerator A left parenthesis x plus 2 right parenthesis left parenthesis x minus 2 right parenthesis over denominator x left parenthesis x plus 2 right parenthesis left parenthesis x minus 2 right parenthesis end fraction plus fraction numerator B x left parenthesis x minus 2 right parenthesis over denominator x left parenthesis x plus 2 right parenthesis left parenthesis x minus 2 right parenthesis end fraction minus fraction numerator C x left parenthesis x plus 2 right parenthesis over denominator x left parenthesis x plus 2 right parenthesis left parenthesis x minus 2 right parenthesis end fraction end cell row blank equals cell fraction numerator A left parenthesis x plus 2 right parenthesis left parenthesis x minus 2 right parenthesis over denominator x cubed minus 4 x squared end fraction plus fraction numerator B x left parenthesis x minus 2 right parenthesis over denominator x cubed minus 4 x squared end fraction minus fraction numerator C x left parenthesis x plus 2 right parenthesis over denominator x cubed minus 4 x squared end fraction end cell row blank equals cell negative fraction numerator A left parenthesis x plus 2 right parenthesis left parenthesis x minus 2 right parenthesis over denominator 4 x squared minus x cubed end fraction minus fraction numerator B x left parenthesis x minus 2 right parenthesis over denominator 4 x squared minus x cubed end fraction plus fraction numerator C x left parenthesis x plus 2 right parenthesis over denominator 4 x squared minus x cubed end fraction end cell row blank equals cell fraction numerator left parenthesis negative A plus B plus C right parenthesis x squared plus left parenthesis 2 B plus 2 C right parenthesis x plus 4 a over denominator 4 x squared minus x cubed end fraction end cell end table

Karena ruas kanan dan ruas kiri sudah memiliki bentuk yang sama, maka

table attributes columnalign right center left columnspacing 0px end attributes row cell 4 A end cell equals 8 row A equals 2 end table

table attributes columnalign right center left columnspacing 0px end attributes row cell negative A minus B plus C end cell equals 5 row cell negative 2 minus B plus C end cell equals 5 row cell negative B plus C end cell equals cell 7 space left parenthesis Persamaan space straight I right parenthesis end cell end table

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 B plus 2 C end cell equals 6 row cell B plus C end cell equals cell 3 space left parenthesis persamaan space II right parenthesis end cell end table

Selanjutnya dengan mengeliminasi persamaan space straight I space dan space II diperoleh:

stack attributes charalign center stackalign right end attributes row minus B plus C equals 7 none end row row minus left parenthesis B plus C right parenthesis equals 3 none end row horizontal line row minus 2 B equals 4 none end row row B equals negative 2 end row end stack

Sehingga,

table attributes columnalign right center left columnspacing 0px end attributes row cell B plus C end cell equals 3 row cell negative 2 plus C end cell equals 3 row C equals cell 3 plus 2 end cell row C equals 5 end table


Jadi, nilai A comma space B comma space dan space C berturut-turut adalah 2 comma space minus 2 comma space dan space 5.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 03 Juni 2021

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