Question

A = (1/x-2 + 2x/x2-4 +1/x+2) x ( 2/x - 1)

a) Rút gọn A

b) Tìm x để A=1

Answer 1

a) Ta có: \(A=\left(\dfrac{1}{x-2}+\dfrac{2x}{x^2-4}+\dfrac{1}{x+2}\right)\cdot\left(\dfrac{2}{x}-1\right)\)

\(=\dfrac{x+2+2x+x-2}{\left(x-2\right)\left(x+2\right)}\cdot\dfrac{2-x}{x}\)

\(=\dfrac{4x}{\left(x-2\right)\left(x+2\right)}\cdot\dfrac{-\left(x-2\right)}{x}\)

\(=\dfrac{-4}{x+2}\)

b) Để A=1 thì x+2=-4

hay x=-6(nhận)