Answer
The simplified form of the given expression = $\frac{x^{2} + 2 x + 15}{x^{2} - 9}$
Work Step by Step
$\frac{x}{x + 3}$ + $\frac{5}{x - 3}$
For addition of two fractional terms take L.C.M of denominator of both terms and add them.
L.C.M of denominator terms[(x + 3) and (x - 3)] = $x^{2}$ - 9
$\frac{x(x-3) + 5(x+3)}{x^{2} - 9}$
= $\frac{x^{2}-3x + 5x+15}{x^{2} - 9}$
= $\frac{x^{2} + 2 x + 15}{x^{2} - 9}$
The simplified form of the given expression = $\frac{x^{2} + 2 x + 15}{x^{2} - 9}$
