solve for X

solve for X
\dfrac{x+2}{x^2-2x} - \dfrac{2}{x-2}=-1

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

\(\begin{array}{|rcll|} \hline \dfrac{x+2}{x^2-2x} - \dfrac{2}{x-2} &=& -1 \quad | \quad x-2 \ne 0 \Rightarrow x \ne 2 \\\\ && \quad | \quad x^2-2x \ne 0 \Rightarrow x \ne 2 \\\\ \dfrac{(x+2)(x-2)-2(x^2-2x)}{(x^2-2x)(x-2)} &=& -1 \\\\ (x+2)(x-2)-2(x^2-2x) &=& -(x^2-2x)(x-2) \\ x^2-4-2x^2+4x &=& -(x^2-2x)(x-2) \\ -x^2+4x-4 &=& -(x^2-2x)(x-2) \quad | \quad \cdot (-1) \\ x^2-4x+4 &=& (x^2-2x)(x-2) \\ (x-2)(x-2) &=& (x^2-2x)(x-2) \quad | \quad : (x-2) \\ x-2 &=& x^2-2x \\ x^2-2x &=& x-2 \\ x^2-3x+2 &=& 0 \\ (x-1)(x-2) &=& 0 \\\\ x = 1 && x \ne 2 \\ \hline \end{array}\)

Solve for x:
(x + 2)/(x^2 - 2 x) - 2/(x - 2) = -1

Bring (x + 2)/(x^2 - 2 x) - 2/(x - 2) together using the common denominator x:
-1/x = -1

Take the reciprocal of both sides:
-x = -1

Multiply both sides by -1:

x = 1