Question

Cho biểu thức P = (x+1/1-x - 1-x/1+x - 4x^2/x^2-1) : 4x^2-4/x^2-2x+1

a) rut gon bieu thức P

b) Tìm giá trị P khi x=5/8

c) tìm x nguyên để P có gtri nguyen

Answer 1

a: \(P=\left(\dfrac{-\left(x+1\right)}{x-1}+\dfrac{x-1}{x+1}-\dfrac{4x^2}{\left(x-1\right)\left(x-1\right)}\right)\cdot\dfrac{\left(x-1\right)^2}{4\left(x-1\right)\left(x+1\right)}\)

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

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

\(=\dfrac{-4x\left(x+1\right)}{x+1}\cdot\dfrac{1}{4\left(x+1\right)}=\dfrac{-x}{x+1}\)

b: khi x=5/8 thì \(P=\left(-\dfrac{5}{8}\right):\dfrac{13}{8}=\dfrac{-5}{13}\)

c: Để P là số nguyên thì \(-x-1+1⋮x+1\)

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

hay \(x\in\left\{0;-2\right\}\)