5. Solve the inequality $\sqrt{\frac{x}{1-x}}-2 \sqrt[4]{\frac{1-x}{x}} \leq 1-\frac{1}{x}$.
# Solution

Let $\sqrt[4]{\frac{1-x}{x}}=t$. Then the original inequality transforms into the system of inequalities

$$
\left\{\frac{\left(t^{3}-1\right)^{2}}{t^{2}} \leq 0\right.
$$

the solution to which is only $t=1$.

Solving the equation $\sqrt[4]{\frac{1-x}{x}}=1$, we find $x=\frac{1}{2}$.

## Grading Criteria

A correct and justified solution - 7 points.

A computational error is made, but the solution is correctly carried to the end (may result in an incorrect answer) - 1 point.

An error in transformations is made, which distorted the solution process - 0 points. In an equivalent transition (in a solution similar to the author's), the condition $t \geq$ 0 is lost - 4 points.