Solve x/x-6=x-2/x-3

$$\frac { x } { x - 6 } = \frac { x - 2 } { x - 3 }$$

Solve for x

$$x = \frac{12}{5} = 2\frac{2}{5} = 2.4$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values 3,6 since division by zero is not defined. Multiply both sides of the equation by \left(x-6\right)\left(x-3\right), the least common multiple of x-6,x-3.

$$\left(x-3\right)x=\left(x-6\right)\left(x-2\right)$$

Use the distributive property to multiply x-3 by x.

$$x^{2}-3x=\left(x-6\right)\left(x-2\right)$$

Use the distributive property to multiply x-6 by x-2 and combine like terms.

$$x^{2}-3x=x^{2}-8x+12$$

Subtract x^{2} from both sides.

$$x^{2}-3x-x^{2}=-8x+12$$

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

$$-3x=-8x+12$$

Add 8x to both sides.

$$-3x+8x=12$$

Combine -3x and 8x to get 5x.

$$5x=12$$

Divide both sides by 5.

$$x=\frac{12}{5}$$