Question

Thực hiện phép tính

a) \(\dfrac{x}{xy-y^2}+\dfrac{2x-y}{xy-x^2}\)

b) \(\dfrac{x^2+2}{x^3-1}+\dfrac{x}{x^2+x+1}+\dfrac{1}{1-x}\)

c) \(\left(x-1\right)-\dfrac{x^2-4}{x+1}\)

d) \(\dfrac{x}{x^2-2x}-\dfrac{x^2+4x}{x^3-4x}-\dfrac{2}{x^2+2x}\)

Answer 1

\(\dfrac{x}{xy-y^2}+\dfrac{2x-y}{xy-x^2}=\dfrac{x-x^2}{xy-x^2-y^2}+\dfrac{2x-y-y^2}{xy-x^2-y^2}=\dfrac{x-x^2+2x-y-y^2}{xy-x^2-y^2}=\dfrac{x^2+2x-y-y^2}{xy-x^2-y^2}\)

Answer 2

b: \(=\dfrac{x^2+2+x^2-x-x^2-x-1}{\left(x-1\right)\left(x^2+x+1\right)}=\dfrac{x^2-2x+1}{\left(x-1\right)\left(x^2+x+1\right)}=\dfrac{x-1}{x^2+x+1}\)

c: \(=\dfrac{x^2-1-x^2+4}{x+1}=\dfrac{3}{x+1}\)

d: \(=\dfrac{1}{x-2}-\dfrac{x+4}{\left(x-2\right)\left(x+2\right)}-\dfrac{2}{x\left(x+2\right)}\)

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

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