Question 132

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

Solution

Expression = $$\ (\frac{x^{2}-x-6}{x^{2}+x-12})\div(\frac{x^{2}+5x+6}{x^{2}+7x+12})$$

= $$\ (\frac{x^{2}-x-6}{x^{2}+x-12})\times(\frac{x^{2}+7x+12}{x^{2}+5x+6})$$

= $$\ (\frac{(x-3)(x+2)}{(x+4)(x-3)})\times(\frac{(x+4)(x+3)}{(x+3)(x+2)})$$

= $$1$$

=> Ans - (A)

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