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14 tháng 12 2021 lúc 19:02
6)
\(\dfrac{3}{2x}+\dfrac{3x-3}{2x-1}+\dfrac{2x^2+1}{4x^2-2x}\)
\(=\dfrac{3}{2x}+\dfrac{3x-3}{2x-1}+\dfrac{2x^2+1}{2x\left(2x-1\right)}\)
\(=\dfrac{3\left(2x-1\right)+\left(3x-3\right).2x+2x^2+1}{2x\left(2x-1\right)}\)
\(=\dfrac{6x-3+6x^2-6x+2x^2+1}{2x\left(2x-1\right)}\)
\(=\dfrac{8x^2-2}{2x\left(2x-1\right)}\)
\(=\dfrac{2\left(4x^2-1\right)}{2x\left(2x-1\right)}\)
\(=\dfrac{2\left(2x+1\right)\left(2x-1\right)}{2\left(2x-1\right)}\)
\(=2x+1\)
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