Question

Giair phương trình

x+1/2x-2 - x-1/2x+2= 2/x²-1

Answer 1

ĐKXĐ: x\(\ne\) 2 và x \(\ne\)-2

\(\dfrac{x+1}{2x-2}\)-\(\dfrac{x-1}{2x+2}\)=\(\dfrac{2}{x^2-1}\)

\(\Leftrightarrow\dfrac{x+1}{2\left(x-1\right)}-\dfrac{x-1}{2\left(x+1\right)}=\dfrac{2}{\left(x-1\right)\left(x+1\right)}\)

\(\Leftrightarrow\left(x+1\right)\left(x+1\right)-\left(x-1\right)\left(x-1\right)=4\)

\(\Leftrightarrow x^2+4x+4-x^2+4x-4=4\)

\(\Leftrightarrow8x=4\)

\(\Leftrightarrow x=\dfrac{1}{2}\)