Question

X^2+1/x+1 + x^2+2/x-2=-2

 

Answer 1

\(\dfrac{x^2+1}{x+1}+\dfrac{x^2+2}{x-2}=-2\) (ĐK: \(x\ne-1;x\ne2\))

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

\(\Leftrightarrow\dfrac{x^3-2x^2+x-2+x^3+x^2+2x+2}{x^2-x-2}=-2\)

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

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

Bấm máy tính, ta có: x = 1 TMĐK

Vậy \(S=\left\{1\right\}\)