Solve 1/x-3+1/x+4=1/x^2+x-12

$$\frac { 1 } { x - 3 } + \frac { 1 } { x + 4 } = \frac { 1 } { x ^ { 2 } + x - 12 }$$

Solve for x

$$x=0$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -4,3 since division by zero is not defined. Multiply both sides of the equation by \left(x-3\right)\left(x+4\right), the least common multiple of x-3,x+4,x^{2}+x-12.

$$x+4+x-3=1$$

Combine x and x to get 2x.

$$2x+4-3=1$$

Subtract 3 from 4 to get 1.

$$2x+1=1$$

Subtract 1 from both sides.

$$2x=1-1$$

Subtract 1 from 1 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.

$$x=0$$