Pertanyaan

Sederhanakanlah! h. x 2 + x − 12 x 2 : 2 x − 6 x 2 + 3 x

Sederhanakanlah!

h. $\frac{x ^{2}}{x ^{2} + x - 12} : \frac{x ^{2} + 3 x}{2 x - 6}$

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S. Yoga

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

bentuk sederhana dari adalah .

bentuk sederhana dari $fraction numerator x squared over denominator x squared plus x minus 12 end fraction space colon space fraction numerator x squared plus 3 x over denominator 2 x minus 6 end fraction$ adalah $fraction numerator 2 x over denominator open parentheses x plus 4 close parentheses open parentheses x plus 3 close parentheses end fraction$ .

Pembahasan

Diketahui bentuk aljabar: Ditanya: bentuk sederhana. Ingat bahwa Mencari bentuk sederhanadari : Jadi, bentuk sederhana dari adalah .

Diketahui bentuk aljabar:

$fraction numerator x squared over denominator x squared plus x minus 12 end fraction space colon space fraction numerator x squared plus 3 x over denominator 2 x minus 6 end fraction$

Ditanya: bentuk sederhana.

Ingat bahwa

$fraction numerator a over b over denominator c over d end fraction equals fraction numerator a times d over denominator b times c end fraction$

Mencari bentuk sederhana dari $fraction numerator x squared over denominator x squared plus x minus 12 end fraction space colon space fraction numerator x squared plus 3 x over denominator 2 x minus 6 end fraction$ :

$fraction numerator x squared over denominator x squared plus x minus 12 end fraction colon thin space fraction numerator x squared plus 3 x over denominator 2 x minus 6 end fraction equals fraction numerator fraction numerator x squared over denominator x squared plus x minus 12 end fraction over denominator fraction numerator x squared plus 3 x over denominator 2 x minus 6 end fraction end fraction equals fraction numerator x squared open parentheses 2 x minus 6 close parentheses over denominator open parentheses x squared plus x minus 12 close parentheses open parentheses x squared plus 3 x close parentheses end fraction equals fraction numerator x squared times thin space 2 open parentheses x minus 3 close parentheses over denominator open parentheses x squared plus x minus 12 close parentheses x open parentheses x plus 3 close parentheses end fraction equals fraction numerator 2 x open parentheses x minus 3 close parentheses over denominator open parentheses x squared plus x minus 12 close parentheses open parentheses x plus 3 close parentheses end fraction equals fraction numerator 2 x open parentheses x minus 3 close parentheses over denominator open parentheses open parentheses x squared minus 3 x close parentheses plus open parentheses 4 x minus 12 close parentheses close parentheses open parentheses x plus 3 close parentheses end fraction equals fraction numerator 2 x open parentheses x minus 3 close parentheses over denominator open parentheses x open parentheses x minus 3 close parentheses plus 4 open parentheses x minus 3 close parentheses close parentheses open parentheses x plus 3 close parentheses end fraction equals fraction numerator 2 x open parentheses x minus 3 close parentheses over denominator open parentheses x minus 3 close parentheses open parentheses x plus 4 close parentheses open parentheses x plus 3 close parentheses end fraction equals fraction numerator 2 x over denominator open parentheses x plus 4 close parentheses open parentheses x plus 3 close parentheses end fraction$

Jadi, bentuk sederhana dari $fraction numerator x squared over denominator x squared plus x minus 12 end fraction space colon space fraction numerator x squared plus 3 x over denominator 2 x minus 6 end fraction$ adalah $fraction numerator 2 x over denominator open parentheses x plus 4 close parentheses open parentheses x plus 3 close parentheses end fraction$ .