Let \( f(x)=\frac{x+1}{x-4} \) and \( g(x)=\frac{-2 x+3}{x^{2}-9 x+20} \) Subtract and simplify: \( f(x)-g(x) \) \( f(x)-g(x)= \) State the domain of \( (f-g)(x) \). Domain: \( \{x \mid x \in \mathbb{R}, x \neq \square \)

Perform the indicated operation. \( \frac{8}{x^{2}-2 x-35}+\frac{7}{x-7} \) \( \frac{8}{x^{2}-2 x-35}+\frac{7}{x-7}=\square( \) Simplify your answer. \( ) \)

Subtract. \[ \frac{3 x}{x^{2}-36}-\frac{2}{x+6} \]

\( \frac{\frac{\frac{2}{x}}{\frac{2}{x^{2}}+\frac{7}{x}}}{\frac{\frac{2}{x}}{\frac{2}{x^{2}}+\frac{7}{x}}=\square \text { (Simplify your answer.) }} \)

Considera la igualdad \( \mathrm{P}=\frac{\mathrm{n}-1}{\mathrm{n}+1} \), con n un número entero. ¿Para cuántos valores distintos de n se cumple que P es un número entero?

\( \frac{\frac{8}{5 x}-\frac{1}{x}}{\frac{4}{5}+\frac{3}{x}} \) \( \frac{\frac{8}{5 x}-\frac{1}{x}}{\frac{4}{5}+\frac{3}{x}}=\square( \) Simplify your answer. \( ) \)