Solve AD/DB=A/E

$$\frac { AD } { DB } = \frac { A } { E }$$

Solve for A

$$\left\{\begin{matrix}A=0\text{, }&D\neq 0\text{ and }B\neq 0\text{ and }E\neq 0\\A\in \mathrm{R}\text{, }&B=E\text{ and }D\neq 0\text{ and }E\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by BDE, the least common multiple of DB,E.

$$EAD=BDA$$

Subtract BDA from both sides.

$$EAD-BDA=0$$

Reorder the terms.

$$-ABD+ADE=0$$

Combine all terms containing A.

$$\left(-BD+DE\right)A=0$$

The equation is in standard form.

$$\left(DE-BD\right)A=0$$

Divide 0 by -BD+DE.

$$A=0$$

Solve for B

$$\left\{\begin{matrix}B=E\text{, }&E\neq 0\text{ and }D\neq 0\\B\neq 0\text{, }&E\neq 0\text{ and }D\neq 0\text{ and }A=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable B cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by BDE, the least common multiple of DB,E.

$$EAD=BDA$$

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

$$BDA=EAD$$

The equation is in standard form.

$$ADB=ADE$$

Divide both sides by AD.

$$\frac{ADB}{AD}=\frac{ADE}{AD}$$

Dividing by AD undoes the multiplication by AD.

$$B=\frac{ADE}{AD}$$

Divide EAD by AD.

$$B=E$$

Variable B cannot be equal to 0.

$$B=E\text{, }B\neq 0$$