\(\dfrac{1}{3x-2}-\dfrac{1}{3x+2}-\dfrac{3x-6}{4-9x^2}\)
\(=\dfrac{1}{3x-2}+\dfrac{-1}{3x+2}+\dfrac{3x-6}{\left(3x-2\right).\left(3x+2\right)}\)
\(=\dfrac{3x+2}{\left(3x-2\right)\left(3x+2\right)}+\dfrac{-\left(3x-2\right)}{\left(3x-2\right)\left(3x+2\right)}+\dfrac{3x-6}{\left(3x-2\right)\left(3x+2\right)}\)
= \(=\dfrac{3x+2-3x+2+3x-6}{\left(3x-2\right)\left(3x+2\right)}\)
\(=\dfrac{3x-2}{\left(3x-2\right)\left(3x+2\right)}\)
\(=\dfrac{1}{3x+2}\)
__-1___ _ _1__ _ _3_x_-_6_
2-3x 2+3x ( 2+3x)(2-3x)
MTC:(2+3x)(2-3x)
_-2-_3x-2+3x-3x+6 =-3x_+_2 =2_-_3x =_1_
(2-3x)(2+3x) (2-3x)(2+3x) (2-3x)(2+3x) 2+3x
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