5. Solve the inequality $\frac{1}{2-x}+\frac{5}{2+x}<1$.

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# Solution:

$\frac{1}{2-x}+\frac{5}{2+x}<1, \frac{2+x+5(2-x)-1(2-x)(2+x)}{(2-x)(2+x)}<0$,

![](https://cdn.mathpix.com/cropped/2024_05_06_8eeeb8d6ace591217257g-20.jpg?height=111&width=572&top_left_y=1778&top_left_x=1393)

$\frac{2+x+10-5x+x^2-4}{(2-x)(2+x)}<0, \frac{x^2-4x+8}{(2-x)(2+x)}<0$

Answer: $(-\infty, -2) \cup (2, +\infty)$.