a) C = \(\left(\frac{2x}{2x^2-5x+3}-\frac{5}{2x-3}\right):\left(3+\frac{2}{1-x}\right)\)
\(=\left(\frac{2x}{\left(2x-3\right)\left(x-1\right)}-\frac{5\left(x-1\right)}{\left(2x-3\right)\left(x-1\right)}\right):\left(\frac{3\left(1-x\right)}{1-x}+\frac{2}{1-x}\right)\)
\(=\left(\frac{2x-5x+5}{\left(2x-3\right)\left(x-1\right)}\right):\left(\frac{3-3x+2}{1-x}\right)\)
\(=\frac{-3x+5}{\left(2x-3\right)\cdot\left(x-1\right)}\cdot\frac{1-x}{-3x+5}=\frac{1-x}{\left(2x-3\right)\left(x-1\right)}=\frac{-1}{2x-3}\)
b) \(\left|2x-1\right|=3\)
\(\Rightarrow\left[{}\begin{matrix}2x-1=3\\2x-1=-3\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}2x=4\\2x=-2\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=2\\x=-1\end{matrix}\right.\)
Với x = 2 ,thay vào C , ta có
C = \(-\frac{1}{2x-3}=\frac{-1}{1}=-1\)
Với x = -1 , thay vào C , ta có
\(C=\frac{-1}{2x-3}=-\frac{1}{-5}\)
c)
C\(>1\Rightarrow\frac{-1}{2x-3}>1\Rightarrow2x-3< -1\Rightarrow2x< 2\Rightarrow x< 1\)
d) \(C=\frac{-1}{2x-3}\ge-1\)
=> C đại GTNN = -1 khi 2x-3 = 1
=> x = 2