Solve x/x-2=4x+8/3x

$$\frac { x } { x - 2 } = \frac { 4 x + 8 } { 3 x }$$

Solve for x

$$x=4$$

$$x=-4$$

Steps by Finding Square Root

Variable x cannot be equal to any of the values 0,2 since division by zero is not defined. Multiply both sides of the equation by 3x\left(x-2\right), the least common multiple of x-2,3x.

$$3xx=\left(x-2\right)\left(4x+8\right)$$

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

$$3x^{2}=\left(x-2\right)\left(4x+8\right)$$

Use the distributive property to multiply x-2 by 4x+8 and combine like terms.

$$3x^{2}=4x^{2}-16$$

Subtract 4x^{2} from both sides.

$$3x^{2}-4x^{2}=-16$$

Combine 3x^{2} and -4x^{2} to get -x^{2}.

$$-x^{2}=-16$$

Divide both sides by -1.

$$x^{2}=\frac{-16}{-1}$$

Fraction \frac{-16}{-1} can be simplified to 16 by removing the negative sign from both the numerator and the denominator.

$$x^{2}=16$$

Take the square root of both sides of the equation.

$$x=4 x=-4$$

Steps Using the Quadratic Formula

Variable x cannot be equal to any of the values 0,2 since division by zero is not defined. Multiply both sides of the equation by 3x\left(x-2\right), the least common multiple of x-2,3x.

$$3xx=\left(x-2\right)\left(4x+8\right)$$

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

$$3x^{2}=\left(x-2\right)\left(4x+8\right)$$

Use the distributive property to multiply x-2 by 4x+8 and combine like terms.

$$3x^{2}=4x^{2}-16$$

Subtract 4x^{2} from both sides.

$$3x^{2}-4x^{2}=-16$$

Combine 3x^{2} and -4x^{2} to get -x^{2}.

$$-x^{2}=-16$$

Add 16 to both sides.

$$-x^{2}+16=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 0 for b, and 16 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\times 16}}{2\left(-1\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1\right)\times 16}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$x=\frac{0±\sqrt{4\times 16}}{2\left(-1\right)}$$

Multiply 4 times 16.

$$x=\frac{0±\sqrt{64}}{2\left(-1\right)}$$

Take the square root of 64.

$$x=\frac{0±8}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{0±8}{-2}$$

Now solve the equation x=\frac{0±8}{-2} when ± is plus. Divide 8 by -2.

$$x=-4$$

Now solve the equation x=\frac{0±8}{-2} when ± is minus. Divide -8 by -2.

$$x=4$$

The equation is now solved.

$$x=-4 x=4$$