\(C=\left(\frac{1}{1-x}+\frac{2}{1+x}-\frac{5-x}{1-x^2}\right):\frac{1-2x}{x^2-1}\)
\(=\frac{x+1+2\left(1-x\right)-5+x}{\left(1-x\right)\left(x+1\right)}:\frac{1-2x}{\left(x-1\right)\left(x+1\right)}\)
\(=\frac{4x-2}{\left(1-x\right)\left(1+x\right)}.\frac{\left(1-x\right)\left(x+1\right)}{2x-1}\)
\(=\frac{2\left(2x-1\right)\left(1-x\right)\left(x+1\right)}{\left(1-x\right)\left(x+1\right)\left(2x-1\right)}=2\)
b, đề có lỗi ko ik
a. \(C=\left(\frac{1}{1-x}+\frac{2}{x+1}-\frac{5-x}{1-x^2}\right):\frac{1-2x}{x^2-1}\)
\(C=\left(\frac{x+1}{1-x^2}+\frac{2-2x}{1-x^2}-\frac{5-x}{1-x^2}\right):\frac{1-2x}{x^2-1}\)
\(C=\frac{-2}{1-x^2}.\frac{x^2-1}{1-2x}\)
\(C=\frac{2}{1-2x}\) ; ĐKXĐ: \(1-2x\ne0\Rightarrow2x\ne1\Rightarrow x\ne\frac{1}{2}\)
b. Để C nguyên thì \(2⋮\left(1-2x\right)\)
\(\Rightarrow1-2x\in\left\{-2;-1;1;2\right\}\)
\(\Rightarrow2x\in\left\{3;2;0;-1\right\}\)
\(\Rightarrow x\in\left\{\frac{3}{2};1;0;\frac{-1}{2}\right\}\) (t/m ĐKXĐ)
