## Task B-1.3.

Solve the equation

$$
\frac{2 x}{x-1}-\frac{x}{x+2}-\frac{5 x}{(x-1)(x+2)}=\frac{4}{x^{2}+x-2}-\frac{2}{x-1}
$$
## Solution.

Let's write the trinomial $x^{2}+x-2$ in the form of a product:

$$
x^{2}+x-2=(x+2)(x-1)
$$

Then the given equation becomes

$$
\frac{2 x(x+2)-x(x-1)-5 x}{(x-1)(x+2)}=\frac{4-2(x+2)}{(x-1)(x+2)}, \quad x \neq 1, x \neq-2
$$

Then we have

$$
\begin{array}{cc}
2 x^{2}+4 x-x^{2}+x-5 x=4-2 x-4 & 1 \text { point } \\
x^{2}+2 x=0 & \\
x(x+2)=0 . & 1 \text { point }
\end{array}
$$

Since $x \neq-2$, the only solution is $x=0$.