What is the value of left(frac{x^{2}-x-6}{x^{ | vedclass

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Question

(A) To simplify:
$\left(\frac{x^{2}-x-6}{x^{2}+x-12}\right) \div \left(\frac{x^{2}+5x+6}{x^{2}+7x+12}\right)$
Convert division into multiplication:

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(A) To simplify:
$\left(\frac{x^{2}-x-6}{x^{2}+x-12}ight) \div \left(\frac{x^{2}+5x+6}{x^{2}+7x+12}ight)$
Convert division into multiplication:
$= \frac{x^{2}-x-6}{x^{2}+x-12} 	imes \frac{x^{2}+7x+12}{x^{2}+5x+6}$
Factorize:
$x^{2}-x-6 = (x-3)(x+2)$
$x^{2}+x-12 = (x+4)(x-3)$
$x^{2}+7x+12 = (x+4)(x+3)$
$x^{2}+5x+6 = (x+3)(x+2)$
Substitute:
$= \frac{(x-3)(x+2)}{(x+4)(x-3)} 	imes \frac{(x+4)(x+3)}{(x+3)(x+2)}$
Cancel common factors:
$= 1$

What is the value of $\left(\frac{x^{2}-x-6}{x^{2}+x-12}\right) \div \left(\frac{x^{2}+5x+6}{x^{2}+7x+12}\right)?$

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