Question

Reduce the expression $\frac{1}{\frac{1}{x-4}-\frac{1}{x+6}}$ in simplified form.

• A. $10$
• B. $\frac{10(x-4)}{x+6}$
• C. $\frac{10}{x^2+2x-24}$
• D. $\frac{x^2+2x-24}{10}$

Answer 1

Answer: (D)

$\frac{x^2+2x-24}{10}$

The expression is $\Rightarrow \frac{1}{\frac{1}{x-4}-\frac{1}{x+6}}$

$\Rightarrow \frac{1}{\frac{x+6-x+4}{(x-4)(x-6)}}$

$\Rightarrow \frac{1}{\frac{10}{x^2+2x-24}}$

$\Rightarrow \frac{x^2+2x-24}{10}$