Pertanyaan

Hasil dari 4 x 2 − 9 2 x 2 + 3 x − 9 × x 2 + 5 x + 6 2 x 2 − x − 6 adalah ....

Hasil dari $\frac{2 x ^{2} + 3 x - 9}{4 x ^{2} - 9} \times \frac{2 x ^{2} - x - 6}{x ^{2} + 5 x + 6}$ adalah ....

$begin mathsize 14px style fraction numerator x minus 2 over denominator x plus 2 end fraction straight dengan straight x not equal to plus-or-minus 3 over 2 comma x not equal to negative 2 comma x not equal to negative 3 end style$
$begin mathsize 14px style fraction numerator x plus 2 over denominator x minus 2 end fraction straight dengan straight x not equal to plus-or-minus 3 over 2 comma x not equal to negative 2 comma x not equal to negative 3 end style$

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah A.

Pembahasan

Ingat aturan pembagian dua pecahan berikut ini. Oleh karena itu didapat Ingat kembali bahwa penyebut suatu pecahan tidak boleh sama dengan, maka dan Dengan demikian, hasil dari adalah . Jadi, jawaban yang tepat adalah A.

Ingat aturan pembagian dua pecahan berikut ini.

$begin mathsize 14px style straight a over straight b divided by straight c over straight d equals straight a over straight b cross times straight d over straight c equals fraction numerator straight a cross times straight d over denominator straight b cross times straight c end fraction end style$

Oleh karena itu didapat

$begin mathsize 14px style fraction numerator 2 straight x squared plus 3 straight x minus 9 over denominator 4 straight x squared minus 9 end fraction times fraction numerator 2 straight x squared minus straight x minus 6 over denominator straight x squared plus 5 straight x plus 6 end fraction equals fraction numerator left parenthesis 2 straight x minus 3 right parenthesis left parenthesis straight x plus 3 right parenthesis over denominator left parenthesis 2 straight x minus 3 right parenthesis left parenthesis 2 straight x plus 3 right parenthesis end fraction times fraction numerator left parenthesis 2 straight x plus 3 right parenthesis left parenthesis straight x minus 2 right parenthesis over denominator left parenthesis straight x plus 2 right parenthesis left parenthesis straight x plus 3 right parenthesis end fraction equals fraction numerator left parenthesis straight x plus 3 right parenthesis over denominator left parenthesis 2 straight x plus 3 right parenthesis end fraction times fraction numerator left parenthesis 2 straight x plus 3 right parenthesis left parenthesis straight x minus 2 right parenthesis over denominator left parenthesis straight x plus 2 right parenthesis left parenthesis straight x plus 3 right parenthesis end fraction equals fraction numerator left parenthesis straight x plus 3 right parenthesis over denominator 1 end fraction times fraction numerator left parenthesis straight x minus 2 right parenthesis over denominator left parenthesis straight x plus 3 right parenthesis left parenthesis straight x plus 3 right parenthesis end fraction equals fraction numerator straight x minus 2 over denominator straight x plus 2 end fraction end style$

Ingat kembali bahwa penyebut suatu pecahan tidak boleh sama dengan, maka

begin mathsize 14px style 4 straight x squared minus 9 not equal to 0 left parenthesis 2 straight x minus 3 right parenthesis left parenthesis 2 straight x plus 3 right parenthesis not equal to 0 straight x not equal to 3 over 2 comma space straight x not equal to negative 3 over 2 end style

dan

begin mathsize 14px style straight x squared plus 5 straight x plus 6 not equal to 0 left parenthesis straight x plus 2 right parenthesis left parenthesis straight x plus 3 right parenthesis not equal to 0 straight x not equal to negative 2 comma space straight x not equal to negative 3 end style

Dengan demikian, hasil dari $begin mathsize 14px style fraction numerator 2 x squared plus 3 x minus 9 over denominator 4 x squared minus 9 end fraction cross times fraction numerator 2 x squared minus x minus 6 over denominator x squared plus 5 x plus 6 end fraction end style$ adalah $begin mathsize 14px style fraction numerator x minus 2 over denominator x plus 2 end fraction straight dengan straight x not equal to plus-or-minus 3 over 2 comma x not equal to negative 2 comma x not equal to negative 3 end style$ .

Jadi, jawaban yang tepat adalah A.