Question

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

Answer 1

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

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

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

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