Solve for x
x=-\frac{e^{y}-1}{y-1}
y\neq 1
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xy+e^{y}-x=1
Subtract x from both sides.
xy-x=1-e^{y}
Subtract e^{y} from both sides.
\left(y-1\right)x=1-e^{y}
Combine all terms containing x.
\frac{\left(y-1\right)x}{y-1}=\frac{1-e^{y}}{y-1}
Divide both sides by y-1.
x=\frac{1-e^{y}}{y-1}
Dividing by y-1 undoes the multiplication by y-1.
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