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\frac{1}{x}=\frac{2}{3}
Reorder the terms.
3=2x
Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 3x, the least common multiple of x,3.
2x=3
Swap sides so that all variable terms are on the left hand side.
x=\frac{3}{2}
Divide both sides by 2.