Solve AD/AB=AE/AC

$$\frac { A D } { A B } = \frac { A E } { A C }$$

Solve for A

$$A\neq 0$$

$$\left(B\neq 0\text{ and }D=0\text{ and }E=0\text{ and }C\neq 0\right)\text{ or }\left(B=\frac{CD}{E}\text{ and }C\neq 0\text{ and }D\neq 0\text{ and }E\neq 0\right)$$

Steps for Solving Linear Equation

Variable A cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by ABC, the least common multiple of AB,AC.

$$CAD=BAE$$

Subtract BAE from both sides.

$$CAD-BAE=0$$

Reorder the terms.

$$-ABE+ACD=0$$

Combine all terms containing A.

$$\left(-BE+CD\right)A=0$$

The equation is in standard form.

$$\left(CD-BE\right)A=0$$

Divide 0 by DC-EB.

$$A=0$$

Variable A cannot be equal to 0.

$$A\in \emptyset$$

Solve for B

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

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 ABC, the least common multiple of AB,AC.

$$CAD=BAE$$

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

$$BAE=CAD$$

The equation is in standard form.

$$AEB=ACD$$

Divide both sides by AE.

$$\frac{AEB}{AE}=\frac{ACD}{AE}$$

Dividing by AE undoes the multiplication by AE.

$$B=\frac{ACD}{AE}$$

Divide CAD by AE.

$$B=\frac{CD}{E}$$

Variable B cannot be equal to 0.

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