Solve 12/4+x+12/4-x=8

$$\frac { 12 } { 4 + x } + \frac { 12 } { 4 - x } = 8$$

Solve for x

$$x=-2$$

$$x=2$$

Steps by Finding Square Root

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

$$\left(x-4\right)\times 12-\left(4+x\right)\times 12=8\left(x-4\right)\left(x+4\right)$$

Use the distributive property to multiply x-4 by 12.

$$12x-48-\left(4+x\right)\times 12=8\left(x-4\right)\left(x+4\right)$$

Multiply -1 and 12 to get -12.

$$12x-48-12\left(4+x\right)=8\left(x-4\right)\left(x+4\right)$$

Use the distributive property to multiply -12 by 4+x.

$$12x-48-48-12x=8\left(x-4\right)\left(x+4\right)$$

Subtract 48 from -48 to get -96.

$$12x-96-12x=8\left(x-4\right)\left(x+4\right)$$

Combine 12x and -12x to get 0.

$$-96=8\left(x-4\right)\left(x+4\right)$$

Use the distributive property to multiply 8 by x-4.

$$-96=\left(8x-32\right)\left(x+4\right)$$

Use the distributive property to multiply 8x-32 by x+4 and combine like terms.

$$-96=8x^{2}-128$$

Swap sides so that all variable terms are on the left hand side.

$$8x^{2}-128=-96$$

Add 128 to both sides.

$$8x^{2}=-96+128$$

Add -96 and 128 to get 32.

$$8x^{2}=32$$

Divide both sides by 8.

$$x^{2}=\frac{32}{8}$$

Divide 32 by 8 to get 4.

$$x^{2}=4$$

Take the square root of both sides of the equation.

$$x=2 x=-2$$

Steps Using the Quadratic Formula

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

$$\left(x-4\right)\times 12-\left(4+x\right)\times 12=8\left(x-4\right)\left(x+4\right)$$

Use the distributive property to multiply x-4 by 12.

$$12x-48-\left(4+x\right)\times 12=8\left(x-4\right)\left(x+4\right)$$

Multiply -1 and 12 to get -12.

$$12x-48-12\left(4+x\right)=8\left(x-4\right)\left(x+4\right)$$

Use the distributive property to multiply -12 by 4+x.

$$12x-48-48-12x=8\left(x-4\right)\left(x+4\right)$$

Subtract 48 from -48 to get -96.

$$12x-96-12x=8\left(x-4\right)\left(x+4\right)$$

Combine 12x and -12x to get 0.

$$-96=8\left(x-4\right)\left(x+4\right)$$

Use the distributive property to multiply 8 by x-4.

$$-96=\left(8x-32\right)\left(x+4\right)$$

Use the distributive property to multiply 8x-32 by x+4 and combine like terms.

$$-96=8x^{2}-128$$

Swap sides so that all variable terms are on the left hand side.

$$8x^{2}-128=-96$$

Add 96 to both sides.

$$8x^{2}-128+96=0$$

Add -128 and 96 to get -32.

$$8x^{2}-32=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 8 for a, 0 for b, and -32 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 8\left(-32\right)}}{2\times 8}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 8\left(-32\right)}}{2\times 8}$$

Multiply -4 times 8.

$$x=\frac{0±\sqrt{-32\left(-32\right)}}{2\times 8}$$

Multiply -32 times -32.

$$x=\frac{0±\sqrt{1024}}{2\times 8}$$

Take the square root of 1024.

$$x=\frac{0±32}{2\times 8}$$

Multiply 2 times 8.

$$x=\frac{0±32}{16}$$

Now solve the equation x=\frac{0±32}{16} when ± is plus. Divide 32 by 16.

$$x=2$$

Now solve the equation x=\frac{0±32}{16} when ± is minus. Divide -32 by 16.

$$x=-2$$

The equation is now solved.

$$x=2 x=-2$$