[tex]\displaystyle d)
\frac{-125}{x^2-5}+ \frac{x^2}{x-5} = ~~~(unde~~ x \neq 0~si ~ x \neq 5) \\ \\
= \frac{-125}{x(x-5)}+ \frac{x^2}{x-5} =
= \frac{-125}{x(x-5)}+ \frac{x \cdot x^2}{x(x-5)} = \frac{x^3-125}{x(x-5)}= \\ \\
= \frac{(x-5)(x^2+5x+25) }{x(x-5)}= \boxed{\frac{x^2+5x+25 }{x}}[/tex]
[tex]\displaystyle f) \\
\left(\frac{1}{x-1} \right)^{-1}+ \frac{x}{x+1} - \frac{x+2}{x^2 - 1} = \\ \\
=\frac{x-1}{1}+ \frac{x}{x+1} - \frac{x+2}{x^2 - 1} = \\ \\
=\frac{(x-1)(x^2 - 1)}{x^2 - 1}+ \frac{x(x-1)}{x^2-1} - \frac{x+2}{x^2 - 1} = \\ \\
=\frac{(x-1)(x^2 - 1) + x(x-1) -(x+2)}{x^2 - 1} =\\ \\
=\frac{x^3-x^2 -x + 1 + x^2 -x -x-2}{x^2 - 1} = \\ \\
= \boxed{ \frac{x^3 -3x-1 }{x^2 - 1} }[/tex]
