First, simplify the second fraction.

$\frac{1}{\textit{x}-2}$

Now multiply to equalize the denominators.

$\frac{\textit{x}^{2}-4}{(\textit{x}-3)(\textit{x}+1)(\textit{x}-2)}+\frac{\textit{x}^{2}-2\textit{x}-3}{(\textit{x}-3)(\textit{x}+1)(\textit{x}-2)}$

$\frac{2x^{2}-2\textit{x}-7}{(\textit{x}-3)(\textit{x}+1)(\textit{x}-2}$

See part (a).

Eliminate $x^{2} − x − 6$.

$\frac{x^{2}+6x+8}{x^{2}-x-20}$

Factor each polynomial.

$\frac{(x+2)(x+4)}{(x-5)(x+4)}$

$\frac{x+2}{x-5}$

Remember to flip the second fraction, then multiply.

See part (c).