Question

a) x+1/x-2-x-1/x+2=2(x^2+2)/x^2-4

b) 2/x-3+x-5/x-1=2

Answer 1

a. ĐKXĐ: x khác 2 và x khác -2

\(\dfrac{x+1}{x-2}-\dfrac{x-1}{x+2}=\dfrac{2\left(x^2+2\right)}{x^2-4}\)

\(\Leftrightarrow\dfrac{\left(x+1\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}-\dfrac{\left(x-1\right)\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}=\dfrac{2x^2+4}{\left(x-2\right)\left(x+2\right)}\) \(\Rightarrow x^2+3x+2-x^2+3x-2=2x^2+4\)

\(\Leftrightarrow-2x^2+6x-4=0\)

\(\Leftrightarrow x^2-3x+2=0\)

\(\Leftrightarrow x^2-x-2x+2=0\)

\(\Leftrightarrow x\left(x-1\right)-2\left(x-1\right)=0\)

\(\Leftrightarrow\left(x-1\right)\left(x-2\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=2\left(loại\right)\end{matrix}\right.\)

Vậy.........