Question

Thực hiện phép tính:

B = \(\dfrac{4}{2-x}\) - \(\dfrac{1-2x}{x-3}\) + \(\dfrac{5x-14}{x^2-5x+6}\)

Answer 1

\(B=\dfrac{4}{2-x}-\dfrac{1-2x}{x-3}+\dfrac{5x-14}{x^2-5x+6}\)

\(=\dfrac{-4}{x-2}+\dfrac{2x-1}{x-3}+\dfrac{5x-14}{\left(x-2\right)\left(x-3\right)}\)

\(=\dfrac{-4\left(x-3\right)+\left(2x-1\right)\left(x-2\right)+5x-14}{\left(x-2\right)\left(x-3\right)}\)

\(=\dfrac{-4x+12+2x^2-5x+2+5x-14}{\left(x-2\right)\left(x-3\right)}\)

\(=\dfrac{2x^2-4x}{\left(x-2\right)\left(x-3\right)}=\dfrac{2x}{x-3}\)