Solve x-12/x-6/x=x+6/x-6

$$\frac{ x-12 }{ x } - \frac{ 6 }{ x } = \frac{ x+6 }{ x-6 }$$

Solve for x

$$x = \frac{18}{5} = 3\frac{3}{5} = 3.6$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values 0,6 since division by zero is not defined. Multiply both sides of the equation by x\left(x-6\right), the least common multiple of x,x-6.

$$\left(x-6\right)\left(x-12\right)-\left(x-6\right)\times 6=x\left(x+6\right)$$

Use the distributive property to multiply x-6 by x-12 and combine like terms.

$$x^{2}-18x+72-\left(x-6\right)\times 6=x\left(x+6\right)$$

Use the distributive property to multiply x-6 by 6.

$$x^{2}-18x+72-\left(6x-36\right)=x\left(x+6\right)$$

To find the opposite of 6x-36, find the opposite of each term.

$$x^{2}-18x+72-6x+36=x\left(x+6\right)$$

Combine -18x and -6x to get -24x.

$$x^{2}-24x+72+36=x\left(x+6\right)$$

Add 72 and 36 to get 108.

$$x^{2}-24x+108=x\left(x+6\right)$$

Use the distributive property to multiply x by x+6.

$$x^{2}-24x+108=x^{2}+6x$$

Subtract x^{2} from both sides.

$$x^{2}-24x+108-x^{2}=6x$$

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

$$-24x+108=6x$$

Subtract 6x from both sides.

$$-24x+108-6x=0$$

Combine -24x and -6x to get -30x.

$$-30x+108=0$$

Subtract 108 from both sides. Anything subtracted from zero gives its negation.

$$-30x=-108$$

Divide both sides by -30.

$$x=\frac{-108}{-30}$$

Reduce the fraction \frac{-108}{-30} to lowest terms by extracting and canceling out -6.

$$x=\frac{18}{5}$$