Question

Answer 1

2.

\(B=\dfrac{x}{x-1}+\dfrac{3}{x+1}-\dfrac{6x-4}{x^2-1}\)

\(=\dfrac{x\left(x+1\right)}{x^2-1}+\dfrac{3\left(x-1\right)}{x^2-1}-\dfrac{6x-4}{x^2-1}\)

\(=\dfrac{x^2+x+3x-3-6x+4}{x^2-1}\)

\(=\dfrac{x^2-2x+1}{x^2-1}\)

\(=\dfrac{\left(x-1\right)^2}{\left(x-1\right)\left(x+1\right)}\)

\(=\dfrac{x-1}{x+1}\)

Answer 2

1.

\(A=\dfrac{2.6-1}{6-1}=\dfrac{11}{5}\)

Answer 3

3.

\(P\in Z\Leftrightarrow\dfrac{2x-1}{x-1}.\dfrac{x-1}{x+1}\in Z\)

\(\Leftrightarrow\dfrac{2x-1}{x+1}\in Z\)

\(\Leftrightarrow2-\dfrac{3}{x+1}\in Z\)

\(\Leftrightarrow x+1\inƯ_3=\left\{\pm1;\pm3\right\}\)

\(\Leftrightarrow x+1\in\left\{-4;-2;0;2\right\}\)