Solve x(x-3)+3(x+3)+(x^2-12)/(x-3)(x+3)=0

$$\frac { x ( x - 3 ) + 3 ( x + 3 ) + ( x ^ { 2 } - 12 ) } { ( x - 3 ) ( x + 3 ) } = 0$$

Solve for x

$$x = \frac{\sqrt{6}}{2} \approx 1.224744871$$

$$x = -\frac{\sqrt{6}}{2} \approx -1.224744871$$

Steps by Finding Square Root

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

$$x\left(x-3\right)+3\left(x+3\right)+x^{2}-12=0$$

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

$$x^{2}-3x+3\left(x+3\right)+x^{2}-12=0$$

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

$$x^{2}-3x+3x+9+x^{2}-12=0$$

Combine -3x and 3x to get 0.

$$x^{2}+9+x^{2}-12=0$$

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

$$2x^{2}+9-12=0$$

Subtract 12 from 9 to get -3.

$$2x^{2}-3=0$$

Add 3 to both sides. Anything plus zero gives itself.

$$2x^{2}=3$$

Divide both sides by 2.

$$x^{2}=\frac{3}{2}$$

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

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

$$x\left(x-3\right)+3\left(x+3\right)+x^{2}-12=0$$

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

$$x^{2}-3x+3\left(x+3\right)+x^{2}-12=0$$

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

$$x^{2}-3x+3x+9+x^{2}-12=0$$

Combine -3x and 3x to get 0.

$$x^{2}+9+x^{2}-12=0$$

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

$$2x^{2}+9-12=0$$

Subtract 12 from 9 to get -3.

$$2x^{2}-3=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -3 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-3\right)}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\left(-3\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\left(-3\right)}}{2\times 2}$$

Multiply -8 times -3.

$$x=\frac{0±\sqrt{24}}{2\times 2}$$

Take the square root of 24.

$$x=\frac{0±2\sqrt{6}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±2\sqrt{6}}{4}$$

Now solve the equation x=\frac{0±2\sqrt{6}}{4} when ± is plus.

$$x=\frac{\sqrt{6}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{6}}{4} when ± is minus.

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

The equation is now solved.

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