Solve for F
F=\frac{\sqrt{3x+1}}{x}
x\neq 0\text{ and }x\geq -\frac{1}{3}
Solve for x
\left\{\begin{matrix}x=\frac{\sqrt{4F^{2}+9}+3}{2F^{2}}\text{, }&F>0\\x=-\frac{\sqrt{4F^{2}+9}-3}{2F^{2}}\text{, }&F<0\\x=-\frac{1}{3}\text{, }&F=0\end{matrix}\right.
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xF=\sqrt{3x+1}
The equation is in standard form.
\frac{xF}{x}=\frac{\sqrt{3x+1}}{x}
Divide both sides by x.
F=\frac{\sqrt{3x+1}}{x}
Dividing by x undoes the multiplication by x.
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