Question

Thực hiện phép tính:

a) \(\dfrac{1}{x}\) + \(\dfrac{1}{x+5}\) + \(\dfrac{x-5}{x^2-5x}\)

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

Giúp e với ạ
 

Answer 1

a: \(\dfrac{1}{x}+\dfrac{1}{x+5}+\dfrac{x-5}{x^2-5x}\)

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

\(=\dfrac{2\left(x+5\right)+x}{x\left(x+5\right)}=\dfrac{3x+10}{x\left(x+5\right)}\)

b: ĐKXĐ: \(x\notin\left\{2;-2\right\}\)

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

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

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

Answer 2