a) Rút gọn:
\(A=\left(\dfrac{x}{x^2-4}+\dfrac{1}{x+2}-\dfrac{4}{x-2}\right):\left(\dfrac{1-x}{x-2}\right)\)
\(A=\left(\dfrac{x}{\left(x-2\right)\left(x+2\right)}+\dfrac{1\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}-\dfrac{4\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}\right):\left(\dfrac{1-x}{x-2}\right)\)
\(A=\left(\dfrac{x+x-2-4x-8}{\left(x-2\right)\left(x+2\right)}\right):\left(\dfrac{1-x}{x-2}\right)\)
\(A=\dfrac{-2x-10}{\left(x-2\right)\left(x+2\right)}.\dfrac{x-2}{1-x}\)
\(A=\dfrac{\left(-2x-10\right)\left(x-2\right)}{\left(x-2\right)\left(x+2\right)\left(1-x\right)}\)
b) Tại \(x=-\dfrac{1}{2}\) :
\(A=\dfrac{\left(-2x-10\right)\left(x-2\right)}{\left(x-2\right)\left(x+2\right)\left(1-x\right)}\)
\(A=\dfrac{\left(-2.-\dfrac{1}{2}-10\right)\left(-\dfrac{1}{2}-2\right)}{\left(-\dfrac{1}{2}-2\right)\left(-\dfrac{1}{2}+2\right)\left(1--\dfrac{1}{2}\right)}\)
\(A=-4\)
\(A=\dfrac{-2x-10}{\left(x+2\right)\left(1-x\right)}\)
