Question

1) tính

a) \(\frac{4}{x+2}+\frac{3}{2-x}+\frac{12}{x^2-4}\)

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

c) \(\frac{1}{3x-2}-\frac{4}{3x+2}-\frac{3x-6}{4-9x^2}\)

d) x - 2 - \(\frac{x^2-10}{x+2}\)

e) \(\frac{1}{2x-2y}-\frac{1}{2x+2y}+\frac{y}{y^2-x^2}\)

f) \(\frac{1}{a+1}-\frac{3}{a^3+1}+\frac{3}{a^2-a+1}\)

g) \(\frac{4-2x+x^2}{x+2}-2-x\)

h)\(\frac{1}{x^3-x}-\frac{1}{x^2-x}+\frac{2}{x^2-1}\)

j) \(\frac{1}{2x+3}-\frac{1}{2x-3}+\frac{x-2}{2x^2-x-3}\)

Answer 1

a: \(=\dfrac{4}{x+2}-\dfrac{3}{x-2}+\dfrac{12}{\left(x-2\right)\left(x+2\right)}\)

\(=\dfrac{4x-8-3x-6+12}{\left(x-2\right)\left(x+2\right)}=\dfrac{x-2}{\left(x-2\right)\left(x+2\right)}=\dfrac{1}{x+2}\)

b: \(=\dfrac{6x+3\left(x-1\right)+2\left(x-2\right)}{6}=\dfrac{6x+3x-3+2x-4}{6}=\dfrac{11x-7}{6}\)

c: \(=\dfrac{1}{3x-2}-\dfrac{4}{3x+2}+\dfrac{3x-6}{\left(3x-2\right)\left(3x+2\right)}\)

\(=\dfrac{3x+2-12x+8+3x-6}{\left(3x-2\right)\left(3x+2\right)}=\dfrac{-6x+4}{\left(3x-2\right)\left(3x+2\right)}=\dfrac{-2}{3x+2}\)