Rút gọn $\Large P=\dfrac{10x}{{{x}^{2}}+3x-4}-\dfrac{2x-3}{x+4}+\dfrac

Rút gọn $\Large P=\dfrac{10x}{{{x}^{2}}+3x-4}-\dfrac{2x-3}{x+4}+\dfrac{x+1}{1-x}$

• A. $P=\dfrac{-3x-7}{x+4}$
• B. $P=\dfrac{-3x+7}{x+4}$
• C. $P=\dfrac{-3x+7}{x-4}$
• D. $P=\dfrac{3x+7}{x+4}$

Điều kiện $\Large \left\{ \begin{align}  & x\ne 1 \\  & x\ne 4 \\ \end{align} \right.$

$\Large \begin{align}  P&=\dfrac{10x}{{{x}^{2}}+3x-4}-\dfrac{2x-3}{x+4}+\dfrac{x+1}{1-x} \\  & =\dfrac{10x}{{{x}^{2}}+3x-4}-\dfrac{2x-3}{x+4}-\dfrac{x+1}{x-1} \\  & =\dfrac{10x-\left( 2x-3 \right)\left( x-1 \right)-\left( x+1 \right)\left( x+4 \right)}{\left( x-1 \right)\left( x+4 \right)} \\  & =\dfrac{10x-2{{x}^{2}}+2x+3x-3-{{x}^{2}}-4x-x-4}{\left( x-1 \right)\left( x+4 \right)} \\  & =\dfrac{-3{{x}^{2}}+10x-7}{\left( x-1 \right)\left( x+4 \right)} \\  & =\dfrac{-\left( x-1 \right)\left( 3x-7 \right)}{\left( x-1 \right)\left( x+4 \right)} \\  & =\dfrac{-3x+7}{x+4} \\ \end{align}$