Question

giải ptrình :\(\frac{x+2}{x-2}-\frac{1}{x}=\frac{2}{x\left(x-2\right)}\)

Answer 1

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

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

\(\Leftrightarrow x^2+x-4=0\) 

Làm nốt

Answer 2

\(\frac{x+2}{x-2}-\frac{1}{x}=\frac{2}{x\cdot\left(x-2\right)}\)

\(\frac{x\cdot\left(x+2\right)-\left(x-2\right)}{x\cdot\left(x-2\right)}=\frac{2}{x\cdot\left(x-2\right)}\)

\(\frac{x^2+2x-x+2}{x\cdot\left(x-2\right)}=\frac{2}{x\cdot\left(x-2\right)}\)

\(x^2+x+2=2\)

\(x^2+x=0\)

\(x\cdot\left(x+1\right)=0\)

\(\hept{\begin{cases}x=0\\x+1=0\end{cases}\Rightarrow\hept{\begin{cases}x=0\\x=-1\end{cases}}}\)