\(\frac{3}{2x^2+2x}+\frac{2x-1}{x^2-1}-\frac{2}{x}\\ =\frac{3}{2x\left(x+1\right)}+\frac{2x-1}{\left(x-1\right)\left(x+1\right)}-\frac{2}{x}\\ =\frac{3\left(x-1\right)}{2x\left(x-1\right)\left(x+1\right)}+\frac{\left(2x-1\right)2x}{2x\left(x-1\right)\left(x+1\right)}-\frac{2.2\left(x-1\right)\left(x+1\right)}{2x\left(x-1\right)\left(x+1\right)}\\ =\frac{3x-3}{2x\left(x-1\right)\left(x+1\right)}+\frac{4x^2-2x}{2x\left(x-1\right)\left(x+1\right)}+\frac{-4x^2+4}{2x\left(x-1\right)\left(x+1\right)}\\ =\frac{3x-3+4x^2-2x-4x^2+4}{2x\left(x-1\right)\left(x+1\right)}\\ \frac{x+1}{2x\left(x-1\right)\left(x+1\right)}\\ \frac{1}{2x^2-2x}\)
Bài làm
\(\frac{3}{2x^2+2x}+\frac{2x-1}{x^2-1}-\frac{2}{x}\)
\(=\frac{3}{2x\left(x+1\right)}+\frac{2x-1}{\left(x-1\right)\left(x+1\right)}-\frac{2}{x}\)
\(=\frac{3\left(x-1\right)}{2x\left(x+1\right)\left(x-1\right)}+\frac{\left(2x-1\right).2x}{2x\left(x+1\right)\left(x-1\right)}-\frac{2.2\left(x+1\right)\left(x-1\right)}{2x\left(x+1\right)\left(x-1\right)}\)
\(=\frac{3x-3}{2x\left(x+1\right)\left(x-1\right)}+\frac{4x^2-2x}{2x\left(x+1\right)\left(x-1\right)}-\frac{4x^2-4}{2x\left(x+1\right)\left(x-1\right)}\)
\(=\frac{3x-3+4x^2-2x-4x^2-4}{2x\left(x+1\right)\left(x-1\right)}\)
\(=\frac{x-7}{2x\left(x+1\right)\left(x-1\right)}\)
~ Soát lại xem mik có làm nhầm không nhá, vì mik hay bị làm nhầm lắm ~
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