B3. The expression is $Z=5 a^{-x}\left(1-a^{-x}\right)^{-1}-3 a^{-x}\left(1+a^{-x}\right)^{-1}-2 a^{x}\left(a^{2 x}-1\right)^{-1}$, where $a^{x} \neq 0,1,-1$.

a) Simplify the expression $Z$.

b) Calculate the value of the expression $Z$ for $a=9^{b+c} \cdot 3^{2 b+c}: 27^{\frac{4}{3} b+c+\frac{1}{3}}$ and $x=1$.

19th Knowledge Competition

in mathematics for students of secondary technical and vocational schools

National Competition, April 13, 2019

## Problems for 3rd Year

Time for solving: 120 minutes. In section A, we will award three points for each correct answer, and deduct one point for each incorrect answer. Write your answers for section A in the left table, leave the right table blank.

![](https://cdn.mathpix.com/cropped/2024_06_07_9fbd0ae098c18b73b6bfg-10.jpg?height=165&width=319&top_left_y=657&top_left_x=640)

| B1 | B2 | B3 |
| :--- | :--- | :--- |
|  |  |  |