Solve ax/x+b=y

$$\frac { a x } { x + b } = y$$

Solve for a (complex solution)

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

Steps for Solving Linear Equation

Multiply both sides of the equation by x+b.

$$ax=y\left(x+b\right)$$

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

$$ax=yx+yb$$

The equation is in standard form.

$$xa=xy+by$$

Divide both sides by x.

$$\frac{xa}{x}=\frac{y\left(x+b\right)}{x}$$

Dividing by x undoes the multiplication by x.

$$a=\frac{y\left(x+b\right)}{x}$$

Solve for a

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

Steps for Solving Linear Equation

Multiply both sides of the equation by x+b.

$$ax=y\left(x+b\right)$$

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

$$ax=yx+yb$$

The equation is in standard form.

$$xa=xy+by$$

Divide both sides by x.

$$\frac{xa}{x}=\frac{y\left(x+b\right)}{x}$$

Dividing by x undoes the multiplication by x.

$$a=\frac{y\left(x+b\right)}{x}$$

Solve for b

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