Solve for x
x=\frac{1}{y-3}
y\neq 3
Solve for y
y=3+\frac{1}{x}
x\neq 0
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yx=3x+1
Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.
yx-3x=1
Subtract 3x from both sides.
\left(y-3\right)x=1
Combine all terms containing x.
\frac{\left(y-3\right)x}{y-3}=\frac{1}{y-3}
Divide both sides by y-3.
x=\frac{1}{y-3}
Dividing by y-3 undoes the multiplication by y-3.
x=\frac{1}{y-3}\text{, }x\neq 0
Variable x cannot be equal to 0.
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