Answer
$\dfrac{x}{x^{2}-4}-\dfrac{5}{x^{2}-4x+4}=\dfrac{x^{2}-7x-10}{(x-2)^{2}(x+2)}$
Work Step by Step
$\dfrac{x}{x^{2}-4}-\dfrac{5}{x^{2}-4x+4}$
Factor both rational expressions completely:
$\dfrac{x}{x^{2}-4}-\dfrac{5}{x^{2}-4x+4}=\dfrac{x}{(x-2)(x+2)}-\dfrac{5}{(x-2)^{2}}=...$
Evaluate the substraction of the two rational expressions and simplify:
$...=\dfrac{x(x-2)-5(x+2)}{(x-2)^{2}(x+2)}=\dfrac{x^{2}-2x-5x-10}{(x-2)^{2}(x+2)}=...$
$...=\dfrac{x^{2}-7x-10}{(x-2)^{2}(x+2)}$
