Question

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

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Answer 1

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

\(\Leftrightarrow\frac{2}{x\left(x-2\right)}+\frac{1}{x}-\frac{x+2}{x-2}=0\)

\(\Leftrightarrow\frac{2}{x\left(x-2\right)}+\frac{x-2}{x\left(x-2\right)}+\frac{x\left(x+2\right)}{x\left(x-2\right)}=0\)

\(\Leftrightarrow\frac{2+x-2+x^2+2x}{x\left(x-2\right)}=0\)

\(\Leftrightarrow\frac{x^2+3x}{x\left(x-2\right)}=0\)

\(\Leftrightarrow\frac{x\left(x+3\right)}{x\left(x-2\right)}=0\)

\(\Leftrightarrow\frac{x+3}{x-2}=0\)

\(\Rightarrow x+3=0\left(x-2\ne0\right)\)

\(\Leftrightarrow x=-3\)