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\frac{1}{x}+\frac{1}{2x}=\frac{1}{4}
Divide both sides by 4.
4+2=x
Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 4x, the least common multiple of x,2x,4.
6=x
Add 4 and 2 to get 6.
x=6
Swap sides so that all variable terms are on the left hand side.