Question

Divide the following and write your answer in lowest terms: $\frac{x^2-36}{x^2-49}÷\frac{x+6}{x+7}$

• A. $\frac{x-6}{x-7}$
• B. $\frac{x+6}{x-7}$
• C. $\frac{x-6}{x+7}$
• D. None of these

Answer 1

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

The given expression $\frac{x^2-36}{x^2-49}÷\frac{x+6}{x+7}$can be simplified as shown below:

$=\frac{x^2-36}{x^2-49}÷\frac{x+6}{x+7}$

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

$=\frac{x^2-6^2}{x^2-7^2}\times \frac{x+7}{x+6}$

$=\frac{(x-6)(x+6)}{(x-7)(x+7)}\times \frac{x+7}{x+6}(\because a^2-b^2=(a-b\left)\right(a+b\left)\right)$

$=\frac{(x-6)(x+6)(x+7)}{(x-7)(x+7)(x+6)}$

$=\frac{x-6}{x-7}$

Hence, $\frac{x^2-36}{x^2-49}÷\frac{x+6}{x+7}=\frac{x-6}{x-7}$.