Answer
$$\frac{x^2+5x-2}{x(x+1)(x-1)}$$
Work Step by Step
First, factor the denominators of each term
$$\frac{x+3}{x^2-1}+\frac{2}{x^2+x}=\frac{x+3}{(x+1)(x-1)}+\frac{2}{x(x+1)}$$
Multiply both the numerator and denominator of the first term by $x$ and the second by $(x-1)$ to obtain a common denominator
$$=\frac{x(x+3)}{x(x+1)(x-1)}+\frac{2(x-1)}{x(x+1)(x-1)}$$
Distribute terms in the numerator and add
$$=\frac{x^2+3x+2x-2}{x(x+1)(x-1)}=\frac{x^2+5x-2}{x(x+1)(x-1)}$$
