Solve for x
x=\frac{y}{y+1}
y\neq -1
Solve for y
y=-\frac{x}{x-1}
x\neq 1
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\left(1+y\right)x=y
Combine all terms containing x.
\left(y+1\right)x=y
The equation is in standard form.
\frac{\left(y+1\right)x}{y+1}=\frac{y}{y+1}
Divide both sides by 1+y.
x=\frac{y}{y+1}
Dividing by 1+y undoes the multiplication by 1+y.
x+xy-y=0
Subtract y from both sides.
xy-y=-x
Subtract x from both sides. Anything subtracted from zero gives its negation.
\left(x-1\right)y=-x
Combine all terms containing y.
\frac{\left(x-1\right)y}{x-1}=-\frac{x}{x-1}
Divide both sides by x-1.
y=-\frac{x}{x-1}
Dividing by x-1 undoes the multiplication by x-1.
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