Solve a+x-a/bx=c

$$a + x - \frac { a } { b } x = c$$

Solve for a (complex solution)

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

Steps for Solving Linear Equation

Multiply both sides of the equation by b.

$$b\left(a+x\right)-ax=cb$$

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

$$ba+bx-ax=cb$$

Subtract bx from both sides.

$$ba-ax=cb-bx$$

Combine all terms containing a.

$$\left(b-x\right)a=cb-bx$$

The equation is in standard form.

$$\left(b-x\right)a=bc-bx$$

Divide both sides by b-x.

$$\frac{\left(b-x\right)a}{b-x}=\frac{b\left(c-x\right)}{b-x}$$

Dividing by b-x undoes the multiplication by b-x.

$$a=\frac{b\left(c-x\right)}{b-x}$$

Solve for a

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

Steps for Solving Linear Equation

Multiply both sides of the equation by b.

$$b\left(a+x\right)-ax=cb$$

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

$$ba+bx-ax=cb$$

Subtract bx from both sides.

$$ba-ax=cb-bx$$

Combine all terms containing a.

$$\left(b-x\right)a=cb-bx$$

The equation is in standard form.

$$\left(b-x\right)a=bc-bx$$

Divide both sides by b-x.

$$\frac{\left(b-x\right)a}{b-x}=\frac{b\left(c-x\right)}{b-x}$$

Dividing by b-x undoes the multiplication by b-x.

$$a=\frac{b\left(c-x\right)}{b-x}$$

Solve for b

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

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 b.

$$b\left(a+x\right)-ax=cb$$

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

$$ba+bx-ax=cb$$

Subtract cb from both sides.

$$ba+bx-ax-cb=0$$

Add ax to both sides. Anything plus zero gives itself.

$$ba+bx-cb=ax$$

Combine all terms containing b.

$$\left(a+x-c\right)b=ax$$

The equation is in standard form.

$$\left(x+a-c\right)b=ax$$

Divide both sides by x+a-c.

$$\frac{\left(x+a-c\right)b}{x+a-c}=\frac{ax}{x+a-c}$$

Dividing by x+a-c undoes the multiplication by x+a-c.

$$b=\frac{ax}{x+a-c}$$

Variable b cannot be equal to 0.

$$b=\frac{ax}{x+a-c}\text{, }b\neq 0$$