Question

Giải các phương trình sau :

a) 2/ x²+2x+1 - 5/ x²-2x+1 = 3/ 1-x²

b) |x² - x | = -2x

Answer 1

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

\(\Leftrightarrow2\left(x-1\right)^2-5\left(x+1\right)^2=-3\left(x^2-1\right)\)

\(\Leftrightarrow2x^2-4x+2-5x^2-10x-5+3x^2-3=0\)

=>-14x-6=0

hay x=-3/7

b: \(\left|x^2-x\right|=-2x\)

\(\Leftrightarrow\left\{{}\begin{matrix}x^2-x=4x^2\\x< =0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\left(3x+1\right)=0\\x< =0\end{matrix}\right.\Leftrightarrow x\in\left\{0;-\dfrac{1}{3}\right\}\)