Question

a) \(\dfrac{2a-1}{2a+1}-\dfrac{2a-3}{2a-1}\)

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

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

d) \(\dfrac{x-5}{x^2+3x}+\dfrac{6}{x+3}\)

e) \(x+2+\dfrac{3}{x-2}\)

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

h) \(\dfrac{x+1}{x-3}+\dfrac{-2x^2+2x}{x^2-9}+\dfrac{x-1}{x+3}\)

i) \(\dfrac{x}{x^2-4x}-\dfrac{3}{5x}\)

k) \(\dfrac{1}{xy-x^2}-\dfrac{1}{y^2-xy}\)

Answer 1

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

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

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

d: \(=\dfrac{x-5+6x}{x\left(x+3\right)}=\dfrac{7x-5}{x\left(x+3\right)}\)

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

i: \(=\dfrac{x}{x\left(x-4\right)}-\dfrac{3}{5x}=\dfrac{1}{x-4}-\dfrac{3}{5x}\)

\(=\dfrac{5x-3x+12}{5x\left(x-4\right)}=\dfrac{2x+12}{5x\left(x-4\right)}\)