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9=\frac{xy}{y}
Divide x by \frac{y}{y} by multiplying x by the reciprocal of \frac{y}{y}.
9=x
Cancel out y in both numerator and denominator.
x=9
Swap sides so that all variable terms are on the left hand side.
9=\frac{xy}{y}
Variable y cannot be equal to 0 since division by zero is not defined. Divide x by \frac{y}{y} by multiplying x by the reciprocal of \frac{y}{y}.
\frac{xy}{y}=9
Swap sides so that all variable terms are on the left hand side.
xy=9y
Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by y.
xy-9y=0
Subtract 9y from both sides.
\left(x-9\right)y=0
Combine all terms containing y.
y=0
Divide 0 by x-9.
y\in \emptyset
Variable y cannot be equal to 0.