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\frac{x}{2y}=\frac{34}{40}
Divide both sides by 40.
\frac{x}{2y}=\frac{17}{20}
Reduce the fraction \frac{34}{40} to lowest terms by extracting and canceling out 2.
10x=17y
Multiply both sides of the equation by 20y, the least common multiple of 2y,20.
\frac{10x}{10}=\frac{17y}{10}
Divide both sides by 10.
x=\frac{17y}{10}
Dividing by 10 undoes the multiplication by 10.
\frac{x}{2y}=\frac{34}{40}
Divide both sides by 40.
\frac{x}{2y}=\frac{17}{20}
Reduce the fraction \frac{34}{40} to lowest terms by extracting and canceling out 2.
10x=17y
Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 20y, the least common multiple of 2y,20.
17y=10x
Swap sides so that all variable terms are on the left hand side.
\frac{17y}{17}=\frac{10x}{17}
Divide both sides by 17.
y=\frac{10x}{17}
Dividing by 17 undoes the multiplication by 17.
y=\frac{10x}{17}\text{, }y\neq 0
Variable y cannot be equal to 0.