Question

Thực hiện các phép tính sau:

a) \(\dfrac{3}{2x+6}-\dfrac{x-6}{2x^2+6x}\)

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

Answer 1

a) \(\dfrac{3}{2x+6}-\dfrac{x-6}{2x^2+6x}=\dfrac{3}{2\left(x+3\right)}-\dfrac{x-6}{2x\left(x+3\right)}=\dfrac{3.x}{2\left(x+3\right).x}-\dfrac{x-6}{2x\left(x+3\right)}=\dfrac{3x-x+6}{2x\left(x+3\right)}=\dfrac{2x+6}{2x\left(x+3\right)}=\dfrac{2\left(x+3\right)}{2x\left(x+3\right)}=\dfrac{1}{x}\)

Answer 2

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

a: \(=\dfrac{3}{2\left(x+3\right)}-\dfrac{x-6}{2x\left(x+3\right)}\)

\(=\dfrac{3x-x+6}{2x\left(x+3\right)}=\dfrac{2\left(x+3\right)}{2x\left(x+3\right)}=\dfrac{1}{x}\)