Solve for f
f=\frac{1}{x}
x\neq 0
Solve for x
x=\frac{1}{f}
f\neq 0
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x=xfx
Multiply both sides of the equation by x.
x=x^{2}f
Multiply x and x to get x^{2}.
x^{2}f=x
Swap sides so that all variable terms are on the left hand side.
\frac{x^{2}f}{x^{2}}=\frac{x}{x^{2}}
Divide both sides by x^{2}.
f=\frac{x}{x^{2}}
Dividing by x^{2} undoes the multiplication by x^{2}.
f=\frac{1}{x}
Divide x by x^{2}.
Examples
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Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
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\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
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Limits
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