Question

If $P=\frac{x^2-36}{x^2-49}$ and $Q=\frac{x+6}{x+7}$ then the value of $\frac{P}{Q}$ is:

• A. $\frac{x-6}{x-7}$
• B. $\frac{x-6}{x+7}$
• C. $\frac{x-7}{x+6}$
• D. $\frac{x+6}{x-7}$

Answer 1

The correct option is A $\frac{x-6}{x-7}$

$P=\frac{x^2-36}{x^2-49}=\frac{x^2-6^2}{x^2-7^2}=\frac{(x-6)(x+6)}{(x-7)(x+7)}=\frac{x-6}{x-7}\times \frac{x+6}{x+7}=\frac{x-6}{x-7}\times Q$

$⟹\frac{P}{Q}=\frac{x-6}{x-7}$