[tex]\begin{gathered} \frac{x+5}{x^2-2x-63}+\frac{x^2+3}{x^2+5x-14} \\ \text{expand the denominators} \\ x^2-2x-63=(x+7)(x-9) \\ x^2+5x-14=(x+7)(x-2) \\ \frac{x+5}{(x+7)(x-9)}+\frac{x^2+3}{(x+7)(x-2)} \\ \frac{(x+5)(x-2)+(x-9)(x^2+3)}{(x+7)(x-9)(x-2)} \\ \frac{x^2-2x+5x-10+x^{\text{ 3}}+3x-9x^2-27}{(x+7)(x-9)(x-2)} \\ \frac{x^3-8x^2+6x-37}{(x+7)(x-9)(x-2)} \\ \end{gathered}[/tex]
