Solve x+a/b=d+e/c

$$\frac{ x+a }{ b } = \frac{ d+e }{ c }$$

Solve for a

$$a=\frac{eb+bd-cx}{c}$$

$$b\neq 0\text{ and }c\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by bc, the least common multiple of b,c.

$$c\left(x+a\right)=b\left(d+e\right)$$

Use the distributive property to multiply c by x+a.

$$cx+ca=b\left(d+e\right)$$

Use the distributive property to multiply b by d+e.

$$cx+ca=bd+be$$

Subtract cx from both sides.

$$ca=bd+be-cx$$

The equation is in standard form.

$$ca=eb+bd-cx$$

Divide both sides by c.

$$\frac{ca}{c}=\frac{eb+bd-cx}{c}$$

Dividing by c undoes the multiplication by c.

$$a=\frac{eb+bd-cx}{c}$$

Solve for b

$$\left\{\begin{matrix}b=\frac{c\left(x+a\right)}{d+e}\text{, }&x\neq -a\text{ and }c\neq 0\text{ and }d\neq -e\\b\neq 0\text{, }&d=-e\text{ and }x=-a\text{ and }c\neq 0\end{matrix}\right.$$

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 bc, the least common multiple of b,c.

$$c\left(x+a\right)=b\left(d+e\right)$$

Use the distributive property to multiply c by x+a.

$$cx+ca=b\left(d+e\right)$$

Use the distributive property to multiply b by d+e.

$$cx+ca=bd+be$$

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

$$bd+be=cx+ca$$

Combine all terms containing b.

$$\left(d+e\right)b=cx+ca$$

The equation is in standard form.

$$\left(d+e\right)b=cx+ac$$

Divide both sides by d+e.

$$\frac{\left(d+e\right)b}{d+e}=\frac{c\left(x+a\right)}{d+e}$$

Dividing by d+e undoes the multiplication by d+e.

$$b=\frac{c\left(x+a\right)}{d+e}$$

Variable b cannot be equal to 0.

$$b=\frac{c\left(x+a\right)}{d+e}\text{, }b\neq 0$$