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\frac{3^{\frac{1}{x}}-1}{3^{\frac{1}{x}}+1}m=1
The equation is in standard form.
\frac{\frac{3^{\frac{1}{x}}-1}{3^{\frac{1}{x}}+1}m\left(3^{\frac{1}{x}}+1\right)}{3^{\frac{1}{x}}-1}=\frac{3^{\frac{1}{x}}+1}{3^{\frac{1}{x}}-1}
Divide both sides by \left(3^{x^{-1}}-1\right)\left(3^{x^{-1}}+1\right)^{-1}.
m=\frac{3^{\frac{1}{x}}+1}{3^{\frac{1}{x}}-1}
Dividing by \left(3^{x^{-1}}-1\right)\left(3^{x^{-1}}+1\right)^{-1} undoes the multiplication by \left(3^{x^{-1}}-1\right)\left(3^{x^{-1}}+1\right)^{-1}.