Solve for f
f=x-\frac{2}{x}
x\neq 0
Solve for x
x=\frac{-\sqrt{f^{2}+8}+f}{2}
x=\frac{\sqrt{f^{2}+8}+f}{2}
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fx\times 5x=5x^{3}-10x
Multiply both sides of the equation by 5x.
fx^{2}\times 5=5x^{3}-10x
Multiply x and x to get x^{2}.
5x^{2}f=5x^{3}-10x
The equation is in standard form.
\frac{5x^{2}f}{5x^{2}}=\frac{5x\left(x^{2}-2\right)}{5x^{2}}
Divide both sides by 5x^{2}.
f=\frac{5x\left(x^{2}-2\right)}{5x^{2}}
Dividing by 5x^{2} undoes the multiplication by 5x^{2}.
f=x-\frac{2}{x}
Divide 5x\left(x^{2}-2\right) by 5x^{2}.
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