Multiply both sides by the Least Common Denominator: \(x(x-2)\).
\[x+3(x-2)=2x(x-2)\]
Simplify.
\[4x-6=2{x}^{2}-4x\]
Move all terms to one side.
\[4x-6-2{x}^{2}+4x=0\]
Simplify \(4x-6-2{x}^{2}+4x\) to \(8x-6-2{x}^{2}\).
\[8x-6-2{x}^{2}=0\]
Factor out the common term \(2\).
\[2(4x-3-{x}^{2})=0\]
Factor out the negative sign.
\[2\times -({x}^{2}-4x+3)=0\]
Divide both sides by \(2\).
\[-{x}^{2}+4x-3=0\]
Multiply both sides by \(-1\).
\[{x}^{2}-4x+3=0\]
Factor \({x}^{2}-4x+3\).
Ask: Which two numbers add up to \(-4\) and multiply to \(3\)?
Rewrite the expression using the above.
\[(x-3)(x-1)\]
\[(x-3)(x-1)=0\]
Solve for \(x\).
Ask: When will \((x-3)(x-1)\) equal zero?
When \(x-3=0\) or \(x-1=0\)
Solve each of the 2 equations above.
\[x=3,1\]
\[x=3,1\]
x=3,1
