Answer
$=\displaystyle \frac{2x^{2}+50}{(x-5)(x+5)}, \quad x\neq-5,5$
Work Step by Step
The denominators are different.
Find a common denominator.
LCD=$(x+5)(x- 5)$
$\displaystyle \frac{x+5}{x-5}+\frac{x-5}{x+5}= \displaystyle \frac{(x+5)(x+5)}{(x+5)(x- 5)}+\frac{(x- 5)(x- 5)}{(x+5)(x- 5)}$
$=\displaystyle \frac{x^{2}+10x+25+x^{2}-10x+25}{(x-5)(x+5)}$
$=\displaystyle \frac{2x^{2}+50}{(x-5)(x+5)}$
... exclude values that yield 0 in the denominator:
$x\neq-5,5$
... here, there are no common factors to cancel.
(the numerator = $2(x+25)$ )
$=\displaystyle \frac{2x^{2}+50}{(x-5)(x+5)}, \quad x\neq-5,5$
