Question

\(A=\left(\frac{2x+1}{2x-1}-\frac{2x-1}{2x+1}\right):\frac{8x}{3-6x}\)

a) Rút gọn biểu thức A

b) Tìm x khi A=\(-\frac{3}{4031}\)

Answer 1

a) \(A=\left(\frac{2x+1}{2x-1}-\frac{2x-1}{2x+1}\right):\frac{8x}{3-6x}\left(ĐK:x\ne\pm\frac{1}{2}\right)\)

\(=\frac{\left(2x+1\right)^2-\left(2x-1\right)^2}{\left(2x-1\right)\left(2x+1\right)}:\frac{8x}{3\left(1-2x\right)}\)

\(=\frac{4x^2+4x+1-4x^2+4x-1}{\left(2x-1\right)\left(2x+1\right)}\cdot\frac{3\left(1-2x\right)}{8x}\)

\(=\frac{8x}{\left(2x-1\right)\left(2x+1\right)}\cdot\frac{-3\left(2x-1\right)}{8x}\)

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

b) Với mọi x thuộc ĐKXĐ mà \(A=-\frac{3}{4031}\Leftrightarrow\frac{-3}{2x+1}=\frac{-3}{4031}\Leftrightarrow2x+1=4031\Leftrightarrow x=2015\left(tm\right)\)

Vậy x=2015 thì \(A=-\frac{3}{4031}\)