Solve b/a=b/c-b/a

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

Solve for b (complex solution)

$$\left\{\begin{matrix}b=0\text{, }&c\neq 0\text{ and }a\neq 0\\b\in \mathrm{C}\text{, }&a=2c\text{ and }c\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by ac, the least common multiple of a,c.

$$cb=ab-cb$$

Subtract ab from both sides.

$$cb-ab=-cb$$

Add cb to both sides.

$$cb-ab+cb=0$$

Combine cb and cb to get 2cb.

$$2cb-ab=0$$

Combine all terms containing b.

$$\left(2c-a\right)b=0$$

Divide 0 by 2c-a.

$$b=0$$

Solve for a

$$\left\{\begin{matrix}a=2c\text{, }&c\neq 0\\a\neq 0\text{, }&c\neq 0\text{ and }b=0\end{matrix}\right.$$

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 ac, the least common multiple of a,c.

$$cb=ab-cb$$

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

$$ab-cb=cb$$

Add cb to both sides.

$$ab=cb+cb$$

Combine cb and cb to get 2cb.

$$ab=2cb$$

The equation is in standard form.

$$ba=2bc$$

Divide both sides by b.

$$\frac{ba}{b}=\frac{2bc}{b}$$

Dividing by b undoes the multiplication by b.

$$a=\frac{2bc}{b}$$

Divide 2cb by b.

$$a=2c$$

Variable a cannot be equal to 0.

$$a=2c\text{, }a\neq 0$$

Solve for b

$$\left\{\begin{matrix}b=0\text{, }&c\neq 0\text{ and }a\neq 0\\b\in \mathrm{R}\text{, }&a=2c\text{ and }c\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by ac, the least common multiple of a,c.

$$cb=ab-cb$$

Subtract ab from both sides.

$$cb-ab=-cb$$

Add cb to both sides.

$$cb-ab+cb=0$$

Combine cb and cb to get 2cb.

$$2cb-ab=0$$

Combine all terms containing b.

$$\left(2c-a\right)b=0$$

Divide 0 by 2c-a.

$$b=0$$