Solve f(v)=-1/2v^-1dv

$$f ( v ) = - \frac { 1 } { 2 } v ^ { - 1 } d v$$

Solve for d

$$d=-2fv$$

$$v\neq 0$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$-\frac{1}{2}v^{-1}dv=fv$$

Reorder the terms.

$$-\frac{1}{2}\times \frac{1}{v}dv=fv$$

Multiply both sides of the equation by 2v, the least common multiple of 2,v.

$$-\frac{1}{2}\times 2dv=fv\times 2v$$

Multiply -\frac{1}{2} and 2 to get -1.

$$-dv=fv\times 2v$$

Multiply v and v to get v^{2}.

$$-dv=fv^{2}\times 2$$

The equation is in standard form.

$$\left(-v\right)d=2fv^{2}$$

Divide both sides by -v.

$$\frac{\left(-v\right)d}{-v}=\frac{2fv^{2}}{-v}$$

Dividing by -v undoes the multiplication by -v.

$$d=\frac{2fv^{2}}{-v}$$

Divide 2fv^{2} by -v.

$$d=-2fv$$

Solve for f

$$f=-\frac{d}{2v}$$

$$v\neq 0$$

Steps for Solving Linear Equation

Reorder the terms.

$$fv=-\frac{1}{2}\times \frac{1}{v}dv$$

Multiply both sides of the equation by 2v, the least common multiple of 2,v.

$$fv\times 2v=-\frac{1}{2}\times 2dv$$

Multiply v and v to get v^{2}.

$$fv^{2}\times 2=-\frac{1}{2}\times 2dv$$

Multiply -\frac{1}{2} and 2 to get -1.

$$fv^{2}\times 2=-dv$$

The equation is in standard form.

$$2v^{2}f=-dv$$

Divide both sides by 2v^{2}.

$$\frac{2v^{2}f}{2v^{2}}=-\frac{dv}{2v^{2}}$$

Dividing by 2v^{2} undoes the multiplication by 2v^{2}.

$$f=-\frac{dv}{2v^{2}}$$

Divide -dv by 2v^{2}.

$$f=-\frac{d}{2v}$$