a)ĐKXĐ:x\(\ne\)2;-2
b)A=\(\left[\dfrac{x+2}{2\left(x-2\right)}-\dfrac{2-x}{2\left(x+2\right)}+\dfrac{8}{\left(x-2\right)\left(x+2\right)}\right].\dfrac{x-2}{x-1}\)
A=\(\dfrac{\left(x+2\right)^2-\left(2-x\right)^2+16}{2\left(x-2\right)\left(x+2\right)}.\dfrac{x-2}{x-1}\)
A=\(\dfrac{8x+16}{2\left(x+2\right)}.\dfrac{1}{x-1}\)=\(\dfrac{8\left(x+2\right)}{2\left(x+2\right)}.\dfrac{1}{x-1}\)
A=\(\dfrac{4}{x-1}\)
c) Để A=1\(\Rightarrow\dfrac{4}{x-1}=1\)
\(\Rightarrow4=x-1\)\(\Rightarrow x=5\)
a: ĐKXĐ: \(x\notin\left\{2;-2;1\right\}\)
b: Ta có: \(A=\left(\dfrac{x+2}{2x-4}-\dfrac{2-x}{2x+4}+\dfrac{8}{x^2-4}\right):\dfrac{x-1}{x-2}\)
\(=\dfrac{x^2+4x+4+x^2-4x+4+16}{2\left(x-2\right)\left(x+2\right)}:\dfrac{x-1}{x-2}\)
\(=\dfrac{2x^2+24}{2\left(x-2\right)\left(x+2\right)}\cdot\dfrac{x-2}{x-1}\)
\(=\dfrac{2\left(x^2+12\right)}{2\left(x+2\right)}\cdot\dfrac{1}{x-1}\)
\(=\dfrac{x^2+12}{\left(x+2\right)\left(x-1\right)}\)
