Solve x+12/x=x/x-300

$$\frac { x + 12 } { x } = \frac { x } { x - 300 }$$

Solve for x

$$x = -\frac{25}{2} = -12\frac{1}{2} = -12.5$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values 0,300 since division by zero is not defined. Multiply both sides of the equation by x\left(x-300\right), the least common multiple of x,x-300.

$$\left(x-300\right)\left(x+12\right)=xx$$

Multiply x and x to get x^{2}.

$$\left(x-300\right)\left(x+12\right)=x^{2}$$

Use the distributive property to multiply x-300 by x+12 and combine like terms.

$$x^{2}-288x-3600=x^{2}$$

Subtract x^{2} from both sides.

$$x^{2}-288x-3600-x^{2}=0$$

Combine x^{2} and -x^{2} to get 0.

$$-288x-3600=0$$

Add 3600 to both sides. Anything plus zero gives itself.

$$-288x=3600$$

Divide both sides by -288.

$$x=\frac{3600}{-288}$$

Reduce the fraction \frac{3600}{-288} to lowest terms by extracting and canceling out 144.

$$x=-\frac{25}{2}$$