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

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

Solve for x

$$x=0$$

Steps for Solving Linear Equation

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

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

Subtract x^{2} from both sides.

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

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

$$-5x+6=-3x+6$$

Add 3x to both sides.

$$-5x+6+3x=6$$

Combine -5x and 3x to get -2x.

$$-2x+6=6$$

Subtract 6 from both sides.

$$-2x=6-6$$

Subtract 6 from 6 to get 0.

$$-2x=0$$

Product of two numbers is equal to 0 if at least one of them is 0. Since -2 is not equal to 0, x must be equal to 0.

$$x=0$$