Solve x+2/c=x-3

$$\frac { x + 2 } { c } = x - 3$$

Solve for c

$$c=-\frac{x+2}{3-x}$$

$$x\neq -2\text{ and }x\neq 3$$

Steps for Solving Linear Equation

Variable c cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by c.

$$x+2=cx+c\left(-3\right)$$

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

$$cx+c\left(-3\right)=x+2$$

Combine all terms containing c.

$$\left(x-3\right)c=x+2$$

Divide both sides by x-3.

$$\frac{\left(x-3\right)c}{x-3}=\frac{x+2}{x-3}$$

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

$$c=\frac{x+2}{x-3}$$

Variable c cannot be equal to 0.

$$c=\frac{x+2}{x-3}\text{, }c\neq 0$$

Solve for x

$$x=-\frac{3c+2}{1-c}$$

$$c\neq 1\text{ and }c\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by c.

$$x+2=cx+c\left(-3\right)$$

Subtract cx from both sides.

$$x+2-cx=c\left(-3\right)$$

Subtract 2 from both sides.

$$x-cx=c\left(-3\right)-2$$

Combine all terms containing x.

$$\left(1-c\right)x=c\left(-3\right)-2$$

The equation is in standard form.

$$\left(1-c\right)x=-3c-2$$

Divide both sides by 1-c.

$$\frac{\left(1-c\right)x}{1-c}=\frac{-3c-2}{1-c}$$

Dividing by 1-c undoes the multiplication by 1-c.

$$x=\frac{-3c-2}{1-c}$$

Divide -3c-2 by 1-c.

$$x=-\frac{3c+2}{1-c}$$