Question

Bài 1: (4 điểm) Thực hiện phép tính:

a/  \(\dfrac{x-1}{x+1}-\dfrac{x+1}{x-1}+\dfrac{4}{x^2-1}\)                b/ \(\dfrac{x^3y+xy^3}{x^4y}:\left(x^2+y^2\right)\)

Answer 1

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

Answer 2

\(\dfrac{xy\left(x^2+y^2\right)}{xy\left(x^3\right)}.\dfrac{1}{x^2+y^2}=\dfrac{1}{x^3}\)

Answer 3

a) Ta có: \(\dfrac{x-1}{x+1}-\dfrac{x+1}{x-1}+\dfrac{4}{x^2-1}\)

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

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

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

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