Subtract \(\frac{1}{2}\) from both sides.
\[\frac{5}{x-1}=\frac{1}{3}-\frac{1}{2}\]
Simplify \(\frac{1}{3}-\frac{1}{2}\) to \(-\frac{1}{6}\).
\[\frac{5}{x-1}=-\frac{1}{6}\]
Multiply both sides by \(x-1\).
\[5=-\frac{1}{6}(x-1)\]
Simplify \(\frac{1}{6}(x-1)\) to \(\frac{x-1}{6}\).
\[5=-\frac{x-1}{6}\]
Multiply both sides by \(6\).
\[5\times 6=-x+1\]
Simplify \(5\times 6\) to \(30\).
\[30=-x+1\]
Regroup terms.
\[30=1-x\]
Subtract \(1\) from both sides.
\[30-1=-x\]
Simplify \(30-1\) to \(29\).
\[29=-x\]
Multiply both sides by \(-1\).
\[-29=x\]
Switch sides.
\[x=-29\]
x=-29
