Solve c/a-1-ab/1-a=3

$$\frac { c } { a - 1 } - \frac { a b } { 1 - a } = 3$$

Solve for a

$$\left\{\begin{matrix}a=-\frac{c+3}{b-3}\text{, }&c\neq -b\text{ and }b\neq 3\\a\neq 1\text{, }&c=-3\text{ and }b=3\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable a cannot be equal to 1 since division by zero is not defined. Multiply both sides of the equation by a-1, the least common multiple of a-1,1-a.

$$c+ab=3\left(a-1\right)$$

Use the distributive property to multiply 3 by a-1.

$$c+ab=3a-3$$

Subtract 3a from both sides.

$$c+ab-3a=-3$$

Subtract c from both sides.

$$ab-3a=-3-c$$

Combine all terms containing a.

$$\left(b-3\right)a=-3-c$$

The equation is in standard form.

$$\left(b-3\right)a=-c-3$$

Divide both sides by b-3.

$$\frac{\left(b-3\right)a}{b-3}=\frac{-c-3}{b-3}$$

Dividing by b-3 undoes the multiplication by b-3.

$$a=\frac{-c-3}{b-3}$$

Divide -c-3 by b-3.

$$a=-\frac{c+3}{b-3}$$

Variable a cannot be equal to 1.

$$a=-\frac{c+3}{b-3}\text{, }a\neq 1$$

Solve for b

$$\left\{\begin{matrix}b=\frac{3a-c-3}{a}\text{, }&a\neq 0\text{ and }a\neq 1\\b\in \mathrm{R}\text{, }&a=0\text{ and }c=-3\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by a-1, the least common multiple of a-1,1-a.

$$c+ab=3\left(a-1\right)$$

Use the distributive property to multiply 3 by a-1.

$$c+ab=3a-3$$

Subtract c from both sides.

$$ab=3a-3-c$$

The equation is in standard form.

$$ab=3a-c-3$$

Divide both sides by a.

$$\frac{ab}{a}=\frac{3a-c-3}{a}$$

Dividing by a undoes the multiplication by a.

$$b=\frac{3a-c-3}{a}$$