Solve x/3+3/x=x/12+12/x

$$\frac { x } { 3 } + \frac { 3 } { x } = \frac { x } { 12 } + \frac { 12 } { x }$$

Solve for x

$$x=-6$$

$$x=6$$

Steps by Finding Square Root

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 12x, the least common multiple of 3,x,12.

$$4xx+12\times 3=xx+12\times 12$$

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

$$4xx+12\times 3=x^{2}+12\times 12$$

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

$$4x^{2}+12\times 3=x^{2}+12\times 12$$

Multiply 12 and 3 to get 36.

$$4x^{2}+36=x^{2}+12\times 12$$

Multiply 12 and 12 to get 144.

$$4x^{2}+36=x^{2}+144$$

Subtract x^{2} from both sides.

$$4x^{2}+36-x^{2}=144$$

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

$$3x^{2}+36=144$$

Subtract 36 from both sides.

$$3x^{2}=144-36$$

Subtract 36 from 144 to get 108.

$$3x^{2}=108$$

Divide both sides by 3.

$$x^{2}=\frac{108}{3}$$

Divide 108 by 3 to get 36.

$$x^{2}=36$$

Take the square root of both sides of the equation.

$$x=6 x=-6$$

Steps Using the Quadratic Formula

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 12x, the least common multiple of 3,x,12.

$$4xx+12\times 3=xx+12\times 12$$

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

$$4xx+12\times 3=x^{2}+12\times 12$$

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

$$4x^{2}+12\times 3=x^{2}+12\times 12$$

Multiply 12 and 3 to get 36.

$$4x^{2}+36=x^{2}+12\times 12$$

Multiply 12 and 12 to get 144.

$$4x^{2}+36=x^{2}+144$$

Subtract x^{2} from both sides.

$$4x^{2}+36-x^{2}=144$$

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

$$3x^{2}+36=144$$

Subtract 144 from both sides.

$$3x^{2}+36-144=0$$

Subtract 144 from 36 to get -108.

$$3x^{2}-108=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and -108 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-108\right)}}{2\times 3}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 3\left(-108\right)}}{2\times 3}$$

Multiply -4 times 3.

$$x=\frac{0±\sqrt{-12\left(-108\right)}}{2\times 3}$$

Multiply -12 times -108.

$$x=\frac{0±\sqrt{1296}}{2\times 3}$$

Take the square root of 1296.

$$x=\frac{0±36}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{0±36}{6}$$

Now solve the equation x=\frac{0±36}{6} when ± is plus. Divide 36 by 6.

$$x=6$$

Now solve the equation x=\frac{0±36}{6} when ± is minus. Divide -36 by 6.

$$x=-6$$

The equation is now solved.

$$x=6 x=-6$$