Question

Cho biểu thức

\(C=\left(\frac{1}{1-x}+\frac{2}{x+1}-\frac{5x}{1-x^2}\right):\frac{1-2x}{x^2-1}\)

a, Rút gọn C

b, Tìm x để C có giá trị nguyên

Answer 1

\(C=\left(\frac{1}{1-x}+\frac{2}{x+1}-\frac{5x}{1-x^2}\right):\frac{1-2x}{x^2-1}\)

\(=\left(\frac{1}{1-x}+\frac{2}{x+1}+\frac{-5x}{\left(1-x\right)\left(x+1\right)}\right):\frac{1-2x}{\left(x-1\right)\left(x+1\right)}\)

\(=\left(\frac{x+1+2-2x-5x}{\left(1-x\right)\left(x+1\right)}\right):\frac{1-2x}{\left(x-1\right)\left(x+1\right)}\)

\(=\left(\frac{3-6x}{\left(1-x\right)\left(x+1\right)}\right).\frac{\left(x-1\right)\left(x+1\right)}{1-2x}\)

\(=\frac{3\left(1-2x\right)}{\left(1-x\right)\left(x+1\right)}.\frac{\left(x-1\right)\left(x+1\right)}{1-2x}\)

\(=\frac{3\left(x-1\right)}{1-x}\)

nho k nha