Question 142
We are given an expression in which $x$ is a real number and $x \notin \{-3, -1, 0, 1, 2, 3, 4\}$.
$$
\frac{x^{2}-4x}{5x-5} \cdot \left(\frac{x^{3}+1}{x^{2}+x}-1\right) \cdot \left(\left(1-\frac{3x-3}{x^{2}+x-6}\right) \cdot \left(\frac{6}{x+3}-\frac{1}{x-2}\right)^{-1}-1\right)^{-1}
$$
Simplify it.
$$
\frac{x^{2}-4x}{5x-5} \cdot \left(\frac{x^{3}+1}{x^{2}+x}-1\right) \cdot \left(\left(1-\frac{3x-3}{x^{2}+x-6}\right) \cdot \left(\frac{6}{x+3}-\frac{1}{x-2}\right)^{-1}-1\right)^{-1}
$$
Simplify it.