1-3x/2x + 3x-2/2x-1 + 2-3x/4x2-2x
\(2x;2x-1;4x^2-2x=2x\left(2x-1\right)\)
\(MTC=2x\left(2x-1\right)\)
\(\dfrac{1-3x}{2x}+\dfrac{3x-2}{2x-1}+\dfrac{2-3x}{4x^2-2x}\)
\(=\dfrac{\left(1-3x\right).2x\left(2x-1\right)}{2x\left(2x-1\right)}+\dfrac{\left(3x-2\right).2x}{\left(2x-1\right).2x}+\dfrac{2-3x}{2x\left(2x-1\right)}\)
\(=\dfrac{2x\left(1-3x\right)\left(2x-1\right)+2x\left(2x-2\right)+2-3x}{2x\left(2x-1\right)}\)
\(=\dfrac{-8x^2+4x+4x^2-4x+2-3x}{2x\left(2x-1\right)}\)
\(=\dfrac{-4x^2-3x+2}{2x\left(2x-1\right)}\)
#AEZn8
\(\dfrac{1-3x}{2x}+\dfrac{3x-2}{2x-1}+\dfrac{2-3x}{4x^2-2x}=\dfrac{\left(1-3x\right)\left(2x-1\right)}{2x\left(2x-1\right)}+\dfrac{2x\left(3x-2\right)}{2x\left(2x-1\right)}+\dfrac{2-3x}{2x\left(2x-1\right)}=\dfrac{-6x^2+5x-1}{2x\left(2x-1\right)}+\dfrac{6x^2-4x}{2x\left(2x-1\right)}+\dfrac{2-3x}{2x\left(2x-1\right)}=\dfrac{\left(-6x^2+6x^2\right)+\left(5x-4x-3x\right)+\left(-1+2\right)}{2x\left(2x-1\right)}=\dfrac{-2x}{2x\left(2x-1\right)}=\dfrac{-1}{2x-1}\)
