Answer
$\frac{2(x^{2}+25)}{(x-5)(x+5)} ; x \ne 5,-5;$
Work Step by Step
$\frac{x+5}{x-5} + \frac{x-5}{x+5}$
$=\frac{(x+5)(x+5)+(x-5)(x-5)}{(x-5)(x+5)}; x \ne 5,-5;$
$=\frac{(x+5)^{2}+(x-5)^{2}}{(x-5)(x+5)}; x \ne 5,-5;$
$[(A+B)^{2} = A^{2}+2AB+B^{2}; (A-B)^{2} = A^{2}-2AB+B^{2}$ So,
$(x+5)^{2} = x^{2}+10x+25; (x-5)^{2} = x^{2}-10x+25]$
$=\frac{x^{2}+10x+25+x^{2}-10x+25}{(x-5)(x+5)}; x \ne 5,-5;$
Combine like terms.
$=\frac{2x^{2}+50}{(x-5)(x+5)}; x \ne 5,-5;$
$=\frac{2(x^{2}+25)}{(x-5)(x+5)} ; x \ne 5,-5;$
