Question

$\frac{5}{ {x}^{2} + 2x + 1 } = \frac{2}{1 - {x}^{2} } + \frac{1}{x - 1}$
Помогите плиз​

Answer 1

$\frac{5}{x^2+2x+1}=\frac{2}{1-x^2}+\frac{1}{x-1}\Leftrightarrow \frac{5}{\left ( x+1 \right )^2}+\frac{2}{\left ( x+1 \right )\left ( x-1 \right )}-\frac{1}{x-1}=0\\\frac{5\left ( x-1 \right )+2\left ( x+1 \right )-\left ( x+1 \right )^2}{\left ( x+1 \right )^2\left ( x-1 \right )}=0\Leftrightarrow \frac{x^2-5x+4}{\left ( x+1 \right )^2\left ( x-1 \right )}=0\Leftrightarrow \frac{x-4}{\left ( x+1 \right )^2}=0\Rightarrow x=4$