Multiply both sides by the Least Common Denominator: \(x\).
\[\frac{12}{x}+1=x\]
Multiply both sides by \(x\).
\[12+x={x}^{2}\]
Move all terms to one side.
\[12+x-{x}^{2}=0\]
Multiply both sides by \(-1\).
\[{x}^{2}-x-12=0\]
Factor \({x}^{2}-x-12\).
Ask: Which two numbers add up to \(-1\) and multiply to \(-12\)?
Rewrite the expression using the above.
\[(x-4)(x+3)\]
\[(x-4)(x+3)=0\]
Solve for \(x\).
Ask: When will \((x-4)(x+3)\) equal zero?
When \(x-4=0\) or \(x+3=0\)
Solve each of the 2 equations above.
\[x=4,-3\]
\[x=4,-3\]
x=4,-3
