Solve ellg=D_{2}/D_{1}

$$\ell g = D _ { 2 } / D _ { 1 }$$

Solve for D_1

$$\left\{\begin{matrix}D_{1}=\frac{D_{2}}{gℓ}\text{, }&D_{2}\neq 0\text{ and }g\neq 0\text{ and }ℓ\neq 0\\D_{1}\neq 0\text{, }&\left(ℓ=0\text{ or }g=0\right)\text{ and }D_{2}=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable D_{1} cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by D_{1}.

$$ℓgD_{1}=D_{2}$$

The equation is in standard form.

$$gℓD_{1}=D_{2}$$

Divide both sides by ℓg.

$$\frac{gℓD_{1}}{gℓ}=\frac{D_{2}}{gℓ}$$

Dividing by ℓg undoes the multiplication by ℓg.

$$D_{1}=\frac{D_{2}}{gℓ}$$

Variable D_{1} cannot be equal to 0.

$$D_{1}=\frac{D_{2}}{gℓ}\text{, }D_{1}\neq 0$$

Solve for D_2

$$D_{2}=D_{1}gℓ$$

$$D_{1}\neq 0$$

Solution Steps

Multiply both sides of the equation by D_{1}.

$$ℓgD_{1}=D_{2}$$

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

$$D_{2}=ℓgD_{1}$$