$$f(x)=\frac{1}{x^{2}-5x-14}+\sqrt{\frac{x+1}{x-1}}$$
$\frac{\sqrt{\frac{x+1}{x-1}}x^{2}-5\sqrt{\frac{x+1}{x-1}}x-14\sqrt{\frac{x+1}{x-1}}+1}{\left(x-7\right)\left(x+2\right)}$
