\(\dfrac{x-2}{x+2}-\dfrac{x}{x-2}=\dfrac{10}{x^2-4}\)
\(ĐK:x\ne\pm2\)
\(\Leftrightarrow\dfrac{\left(x-2\right)\left(x-2\right)-x\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}=\dfrac{10}{\left(x-2\right)\left(x+2\right)}\)
\(\Leftrightarrow\left(x-2\right)\left(x-2\right)-x\left(x+2\right)=10\)
\(\Leftrightarrow x^2-4x+4-x^2-2x=10\)
\(\Leftrightarrow-6x=6\)
\(\Leftrightarrow x=-1\left(tm\right)\)
Vậy \(S=\left\{-1\right\}\)
\(\dfrac{\left(x-2\right)}{\left(x+2\right)}-\dfrac{x}{\left(x-2\right)}=\dfrac{10}{\left(^{ }x^2-4\right)}\)
\(\Leftrightarrow\) \(\dfrac{\left(x-2\right)}{\left(x+2\right)}-\dfrac{x}{\left(x-2\right)}=\dfrac{10}{\left(x+2\right)\left(x-2\right)}\)
\(\Leftrightarrow\left(x-2\right)\left(x-2\right)+\left(-x\right)\left(x+2\right)=10\)
\(\Leftrightarrow-6x+4=10\)
\(\Leftrightarrow-6x=10-4\)
\(\Leftrightarrow-6x=6\)
\(\Leftrightarrow x=6:\left(-6\right)\)
\(\Leftrightarrow x=-1\)
