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\frac{1}{4}x-\frac{1}{3}y=A
Swap sides so that all variable terms are on the left hand side.
\frac{1}{4}x=A+\frac{1}{3}y
Add \frac{1}{3}y to both sides.
\frac{1}{4}x=\frac{y}{3}+A
The equation is in standard form.
\frac{\frac{1}{4}x}{\frac{1}{4}}=\frac{\frac{y}{3}+A}{\frac{1}{4}}
Multiply both sides by 4.
x=\frac{\frac{y}{3}+A}{\frac{1}{4}}
Dividing by \frac{1}{4} undoes the multiplication by \frac{1}{4}.
x=\frac{4y}{3}+4A
Divide A+\frac{y}{3} by \frac{1}{4} by multiplying A+\frac{y}{3} by the reciprocal of \frac{1}{4}.