\(A=\left(\frac{1}{1-x}+\frac{2}{x+1}-\frac{5-x}{1-x^2}\right):\frac{1-2x}{x^2-1}\left(x\ne\pm1;x\ne\frac{1}{2}\right)\)
\(\Leftrightarrow A=\left(\frac{-1}{x-1}+\frac{2}{x+1}+\frac{5-x}{x^2-1}\right)\cdot\frac{\left(x-1\right)\left(x+1\right)}{1-2x}\)
\(\Leftrightarrow A=\left[\frac{-x-1}{\left(x-1\right)\left(x+1\right)}+\frac{2x-2}{\left(x-1\right)\left(x+1\right)}+\frac{5-x}{\left(x-1\right)\left(x+1\right)}\right]\cdot\frac{\left(x-1\right)\left(x+1\right)}{1-2x}\)
\(\Leftrightarrow A=\frac{-x-1+2x-2+5-x}{\left(x-1\right)\left(x+1\right)}\cdot\frac{\left(x-1\right)\left(x+1\right)}{2}\)
\(\Leftrightarrow A=\frac{2\left(x-1\right)\left(x+1\right)}{2\left(x-1\right)\left(x+1\right)}=1\)
vậy \(A=1\left(x\ne\pm1;x\ne\frac{1}{2}\right)\)
\(A=\left(\frac{1}{1-x}+\frac{2}{x+1}-\frac{5-x}{1-x^2}\right):\frac{1-2x}{x^2-1}.\)
\(A=\left(\frac{x+1}{\left(1-x\right)\left(x+1\right)}+\frac{2\left(1-x\right)}{\left(x+1\right)\left(1-x\right)}-\frac{5-x}{1-x^2}\right):\frac{1-2x}{x^2-1}.\)
\(A=\left(\frac{x+1}{\left(1-x\right)\left(x+1\right)}+\frac{2\left(1-x\right)}{\left(x+1\right)\left(1-x\right)}-\frac{5-x}{1-x^2}\right):\frac{1-2x}{x^2-1}.\)
\(A=\left(\frac{x+1+2-2x-5+x}{1-x^2}\right):\frac{1-2x}{x^2-1}.\)
\(A=\left(\frac{-2}{1-x^2}\right):\frac{1-2x}{x^2-1}.\)
\(A=\frac{2}{x^2-1}:\frac{1-2x}{x^2-1}.\)
\(A=\frac{2}{x^2-1}\cdot\frac{^2-1}{1-2x}=\frac{2}{1-2x}\)ĐK: x khác 1/2
sửa lại từ dòng thứ 4
\(A=\frac{2}{\left(x-1\right)\left(x+1\right)}\cdot\frac{\left(x-1\right)\left(x+1\right)}{1-2x}=\frac{2}{1-2x}\)
nhìn lại giờ mới thấy thiếu cái điều kiện x khác 1 hi` >: Bạn bổ sung ha
Bài làm:
đkxđ: \(x\ne\pm1\)
\(A=\left(\frac{1}{1-x}+\frac{2}{x+1}-\frac{5-x}{1-x^2}\right)\div\frac{1-2x}{x^2-1}\)
\(A=\left(\frac{1}{1-x}+\frac{2}{x+1}-\frac{5-x}{\left(1-x\right)\left(x+1\right)}\right).\frac{\left(1-x\right)\left(1+x\right)}{2x-1}\)
\(A=\frac{x+1+2\left(1-x\right)-5+x}{\left(1-x\right)\left(1+x\right)}.\frac{\left(1-x\right)\left(1+x\right)}{2x-1}\)
\(A=\frac{-2}{2x-1}\)
\(A=\frac{2}{1-2x}\)
\(A=\left(\frac{1}{1-x}+\frac{2}{x+1}-\frac{5-x}{1-x^2}\right):\frac{1-2x}{x^2-1}\)
ĐKXĐ : \(x\ne\pm1;x\ne\frac{1}{2}\)
\(A=\left(\frac{1+x}{\left(1-x\right)\left(1+x\right)}+\frac{2\left(1-x\right)}{\left(1-x\right)\left(1+x\right)}-\frac{5-x}{\left(1-x\right)\left(1+x\right)}\right):\frac{1-2x}{x^2-1}\)
\(A=\left(\frac{1+x+2-2x-5+x}{\left(1-x\right)\left(1+x\right)}\right):\frac{1-2x}{x^2-1}\)
\(A=\frac{-2}{\left(1-x\right)\left(1+x\right)}\cdot\frac{x^2-1}{1-2x}\)
\(A=\frac{-2\left(x+1\right)\left(x-1\right)}{\left(1-x\right)\left(1+x\right)\left(1-2x\right)}\)
\(A=\frac{-2\left(x-1\right)}{\left(1-x\right)\left(1-2x\right)}\)
\(A=\frac{2\left(1-x\right)}{\left(1-x\right)\left(1-2x\right)}\)
\(A=\frac{2}{1-2x}\)
