Question

Rút gọn phương trình

P = \(\left(\frac{2x}{2x^2-5x+3}-\frac{5}{2x-3}\right):\left(3+\frac{2}{1-x}\right)\)

Answer 1

Ta có: \(P=\left(\frac{2x}{2x^2-5x+3}-\frac{5}{2x-3}\right):\left(3+\frac{2}{1-x}\right)\)

\(=\left(\frac{2x}{\left(x-1\right)\left(2x-3\right)}-\frac{5\left(x-1\right)}{\left(2x-3\right)\left(x-1\right)}\right):\left(3-\frac{2}{x-1}\right)\)

\(=\frac{2x-5\left(x-1\right)}{\left(x-1\right)\left(2x-3\right)}:\frac{3\left(x-1\right)-2}{x-1}\)

\(=\frac{2x-5x+5}{\left(x-1\right)\left(2x-3\right)}\cdot\frac{x-1}{3x-3-2}\)

\(=\frac{-3x+5}{2x-3}\cdot\frac{1}{3x-5}\)

\(=\frac{-\left(3x-5\right)\cdot1}{\left(2x-3\right)\cdot\left(3x-5\right)}\)

\(=\frac{-1}{2x-3}\)

\(=\frac{1}{3-2x}\)