\(P=\left(\frac{2x}{2x^2-5x+2}-\frac{5}{2x-3}\right):\left(3+\frac{2}{1-x}\right) \)(dk x khac 3/2 ; x khac 1)
\(P=\left(\frac{2x}{\left(2x-3\right)\left(x-1\right)}-\frac{5\left(x-1\right)}{\left(2x+3\right)\left(x-1\right)}\right):\left(\frac{3\left(x-1\right)}{x-1}-\frac{2}{x-1}\right)\)
\(P=\frac{2x-5x+5}{\left(2x-3\right)\left(x-1\right)}:\frac{3x-3-2}{x-1}\)
\(P=\frac{-\left(3x-5\right)}{\left(2x-3\right)\left(x-1\right)}\cdot\frac{x-1}{3x-5}\)
\(P=\frac{-1}{2x-3}\)
b) TC: \(|2x-1|=3\)
TH1) \(|2x-1|=2x-1\)khi \(x\ge\frac{1}{2}\)
2x-1=3 suy ra x=2 ( thoa dk)
TH2) \(|2x-1|=-2x+1\)khi \(x< \frac{1}{2}\)
-2x+1=3 suy ra x=-1 ( thoa dk)
khi x= 2 thi P=-1
khi x= -1 thi P=1/5
c) de P thuoc Z thi \(-\frac{1}{2x-3}\)thuoc Z
suy ra \(\frac{1}{3-2x}\)thuoc Z
suy ra 3-2x thuoc \(Ư\left(1\right)\in\left\{\pm1\right\}\)
khi 3-2x=1 thi x= 1 (ko thoa dk x khac 1)
khi 3-2x=-1 thi x=2(thoa dk)
vay x=2 thi P thuoc Z
d) giai tg tu cau c
