Question

tính

b)\(\dfrac{x-1}{x-2}-\dfrac{5}{x+2}-\dfrac{3x^2-8}{x^2-4}\)

c)\(\dfrac{3x-1}{x-1}-\dfrac{2x+5}{x+3}\)

d)\(\dfrac{2}{x\left(x+2\right)}+\dfrac{1}{\left(x+2\right)\left(x+3\right)}+\dfrac{2}{\left(x+3\right)\left(x+5\right)}\)

Answer 1

b: \(=\dfrac{x^2+x-2-5x+10-3x^2+8}{\left(x-2\right)\left(x+2\right)}\)

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

c: \(=\dfrac{3x^2+9x-x-3-2x^2+2x-5x+5}{\left(x+3\right)\left(x-1\right)}\)

\(=\dfrac{x^2+5x+2}{\left(x+3\right)\left(x-1\right)}\)

d: \(=\dfrac{1}{x}-\dfrac{1}{x+2}+\dfrac{1}{x+2}-\dfrac{1}{x+3}+\dfrac{1}{x+3}-\dfrac{1}{x+5}\)

\(=\dfrac{1}{x}-\dfrac{1}{x+5}=\dfrac{x+5-x}{x\left(x+5\right)}=\dfrac{5}{x\left(x+5\right)}\)