Question

Perform the indicated operation : $\frac{x}{x^2-16}-\frac{8}{x^2+5x+4}$

• A. $\frac{x^2-7x+32}{(x-4)(x+4)(x+1)}$
• B. $\frac{x^2-7}{(x-4)(x+4)(x+1)}$
• C. $\frac{x^2-7x+32}{(x-4)(x+4)}$
• D. $\frac{x^2-7x+32}{(x-4)(x-4)(x-1)}$

Answer 1

Answer: (A)

$\frac{x^2-7x+32}{(x-4)(x+4)(x+1)}$

$\frac{x}{x^2-16}-\frac{8}{x^2+5x+4}$ = $\frac{x}{(x+4)(x-4)}-\frac{8}{(x+1)(x+4)}$

LCM of $\left[\right(x+4\left)\right(x-4\left)\right]$ and $\left[\right(x+4\left)\right(x+1\left)\right]$ is $\left[\right(x+4\left)\right(x-4\left)\right(x+1\left)\right]$

= $\frac{x(x+1)-8(x-4)}{(x+4)(x-4)(x+1)}$

= $\frac{x^2+x-8x+32}{(x+4)(x-4)(x+1)}$

= $\frac{x^2-7x+32}{(x+4)(x-4)(x+1)}$