Answer
$\frac{20x-6}{(5x+2)(5x-2)}; x \ne \frac{-2}{5}, \frac{2}{5}$
Work Step by Step
$\frac{3}{5x+2} + \frac{5x}{25x^{2}-4}$
$25x^{2}-4$ is in the form of $(a^{2}-b^{2})$
$(a^{2}-b^{2}) = (a+b)(a-b)$ So,
$25x^{2}-4 = (5x+2)(5x-2)$
The given expression can be written as
$=\frac{3}{5x+2} + \frac{5x}{ (5x+2)(5x-2)}; x \ne \frac{-2}{5}, \frac{2}{5}$
Taking Least Common Denominator,
$=\frac{3(5x-2)+5x}{ (5x+2)(5x-2)}; x \ne \frac{-2}{5}, \frac{2}{5}$
$=\frac{15x-6+5x}{ (5x+2)(5x-2)}; x \ne \frac{-2}{5}, \frac{2}{5}$
Combine like terms
$=\frac{20x-6}{(5x+2)(5x-2)}; x \ne \frac{-2}{5}, \frac{2}{5}$
