Answer
$\dfrac{5}{x-2}+\dfrac{7x}{x^{2}-4}-\dfrac{11}{x}=\dfrac{x^{2}+10x+44}{x(x-2)(x+2)}$
Work Step by Step
$\dfrac{5}{x-2}+\dfrac{7x}{x^{2}-4}-\dfrac{11}{x}$
Factor the denominator of the second fraction:
$\dfrac{5}{x-2}+\dfrac{7x}{x^{2}-4}-\dfrac{11}{x}=\dfrac{5}{x-2}+\dfrac{7x}{(x-2)(x+2)}-\dfrac{11}{x}=...$
Evaluate the indicated operations and simplify:
$...=\dfrac{5x(x+2)+7x(x)-11(x-2)(x+2)}{x(x-2)(x+2)}=...$
$...=\dfrac{5x^{2}+10x+7x^{2}-11x^{2}+44}{x(x-2)(x+2)}=\dfrac{x^{2}+10x+44}{x(x-2)(x+2)}$
