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

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

Solve for x

$$x = \frac{14}{3} = 4\frac{2}{3} \approx 4.666666667$$

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-3,x-6.

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

Use the distributive property to multiply 2 by x-6.

$$\left(2x-12\right)\left(x-3\right)=\left(x-6\right)\left(x+2\right)+\left(x-3\right)\left(x-2\right)$$

Use the distributive property to multiply 2x-12 by x-3 and combine like terms.

$$2x^{2}-18x+36=\left(x-6\right)\left(x+2\right)+\left(x-3\right)\left(x-2\right)$$

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

$$2x^{2}-18x+36=x^{2}-4x-12+\left(x-3\right)\left(x-2\right)$$

Use the distributive property to multiply x-3 by x-2 and combine like terms.

$$2x^{2}-18x+36=x^{2}-4x-12+x^{2}-5x+6$$

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

$$2x^{2}-18x+36=2x^{2}-4x-12-5x+6$$

Combine -4x and -5x to get -9x.

$$2x^{2}-18x+36=2x^{2}-9x-12+6$$

Add -12 and 6 to get -6.

$$2x^{2}-18x+36=2x^{2}-9x-6$$

Subtract 2x^{2} from both sides.

$$2x^{2}-18x+36-2x^{2}=-9x-6$$

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

$$-18x+36=-9x-6$$

Add 9x to both sides.

$$-18x+36+9x=-6$$

Combine -18x and 9x to get -9x.

$$-9x+36=-6$$

Subtract 36 from both sides.

$$-9x=-6-36$$

Subtract 36 from -6 to get -42.

$$-9x=-42$$

Divide both sides by -9.

$$x=\frac{-42}{-9}$$

Reduce the fraction \frac{-42}{-9} to lowest terms by extracting and canceling out -3.

$$x=\frac{14}{3}$$