Pertanyaan

Bentuk sederhana dari 9 x 2 − 4 3 x 2 + 10 x − 8 adalah.... [ UN 2009]

Bentuk sederhana dari $\frac{3 x ^{2} + 10 x - 8}{9 x ^{2} - 4}$ adalah....

[ UN 2009]

$fraction numerator x space plus space 4 over denominator 3 x space plus space 2 end fraction$
$fraction numerator x space plus space 4 over denominator 3 x space minus space 2 end fraction$
$fraction numerator x space minus space 2 over denominator 3 x space minus space 1 end fraction$
$fraction numerator x space minus space 4 over denominator 3 x space minus space 2 end fraction$

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Jawaban terverifikasi

Pembahasan

Lakukan pemfaktorkan dalam bentuk Ingat bahwa Jadi, Sehingga

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3 x squared plus 10 x minus 8 equals 1 third left parenthesis 3 x plus 12 right parenthesis left parenthesis 3 x minus 2 right parenthesis space equals left parenthesis x plus 4 right parenthesis left parenthesis 3 x minus 2 right parenthesis

Ingat bahwa a squared space minus space b to the power of 2 space end exponent space equals space left parenthesis a space plus space b right parenthesis left parenthesis a space minus b right parenthesis

Jadi,

9 x squared minus 4 equals left parenthesis 3 x right parenthesis squared minus 2 squared space equals left parenthesis 3 x plus 2 right parenthesis left parenthesis 3 x minus 2 right parenthesis

Sehingga

$fraction numerator 3 x squared plus 10 x minus 8 over denominator 9 x squared minus 4 end fraction equals fraction numerator left parenthesis x plus 4 right parenthesis left parenthesis 3 x minus 2 right parenthesis over denominator left parenthesis 3 x plus 2 right parenthesis left parenthesis 3 x minus 2 right parenthesis end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator space x plus 4 over denominator 3 x plus 2 end fraction$