d.
\(\Leftrightarrow\frac{2-5x+2\left(x+5\right)}{\left(x+5\right)\left(2-5x\right)}\ge0\)
\(\Leftrightarrow\frac{3\left(4-x\right)}{\left(x+5\right)\left(2-5x\right)}\ge0\Rightarrow\left[{}\begin{matrix}-5< x< \frac{2}{5}\\x\ge4\end{matrix}\right.\)
e.
\(\Leftrightarrow\frac{1}{x+2}+\frac{1}{x-1}-\frac{1}{x-2}\ge0\)
\(\Leftrightarrow\frac{\left(x-1\right)\left(x-2\right)+\left(x+2\right)\left(x-2\right)-\left(x+2\right)\left(x-1\right)}{\left(x+2\right)\left(x-1\right)\left(x-2\right)}\ge0\)
\(\Leftrightarrow\frac{x\left(x-4\right)}{\left(x+2\right)\left(x-1\right)\left(x-2\right)}\ge0\Rightarrow\left[{}\begin{matrix}-2< x\le0\\1< x< 2\\x\ge4\end{matrix}\right.\)
f.
\(\Leftrightarrow\frac{x-2}{x-3}-\frac{x-1}{x+1}>0\)
\(\Leftrightarrow\frac{\left(x-2\right)\left(x+1\right)-\left(x-1\right)\left(x-3\right)}{\left(x+1\right)\left(x-3\right)}>0\Leftrightarrow\frac{3x-5}{\left(x+1\right)\left(x-3\right)}>0\) \(\Rightarrow\left[{}\begin{matrix}-1< x\le\frac{5}{3}\\x>3\end{matrix}\right.\)
