Solve x-2/x-2+x-3/x-3=2x^2/x^2-5x+6

$$\frac { x - 2 } { x - 2 } + \frac { x - 3 } { x - 3 } = \frac { 2 x ^ { 2 } } { x ^ { 2 } - 5 x + 6 }$$

Solve for x

$$x = \frac{6}{5} = 1\frac{1}{5} = 1.2$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values 2,3 since division by zero is not defined. Multiply both sides of the equation by \left(x-3\right)\left(x-2\right), the least common multiple of x-2,x-3,x^{2}-5x+6.

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

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

$$x^{2}-5x+6+\left(x-2\right)\left(x-3\right)=2x^{2}$$

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

$$x^{2}-5x+6+x^{2}-5x+6=2x^{2}$$

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

$$2x^{2}-5x+6-5x+6=2x^{2}$$

Combine -5x and -5x to get -10x.

$$2x^{2}-10x+6+6=2x^{2}$$

Add 6 and 6 to get 12.

$$2x^{2}-10x+12=2x^{2}$$

Subtract 2x^{2} from both sides.

$$2x^{2}-10x+12-2x^{2}=0$$

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

$$-10x+12=0$$

Subtract 12 from both sides. Anything subtracted from zero gives its negation.

$$-10x=-12$$

Divide both sides by -10.

$$x=\frac{-12}{-10}$$

Reduce the fraction \frac{-12}{-10} to lowest terms by extracting and canceling out -2.

$$x=\frac{6}{5}$$