Solve x+1/x=x/4+4/x

$$x + \frac { 1 } { x } = \frac { x } { 4 } + \frac { 4 } { x }$$

Solve for x

$$x=-2$$

$$x=2$$

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 4x, the least common multiple of x,4.

$$4xx+4=xx+4\times 4$$

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

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

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

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

Multiply 4 and 4 to get 16.

$$4x^{2}+4=x^{2}+16$$

Subtract x^{2} from both sides.

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

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

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

Subtract 4 from both sides.

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

Subtract 4 from 16 to get 12.

$$3x^{2}=12$$

Divide both sides by 3.

$$x^{2}=\frac{12}{3}$$

Divide 12 by 3 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 0 since division by zero is not defined. Multiply both sides of the equation by 4x, the least common multiple of x,4.

$$4xx+4=xx+4\times 4$$

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

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

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

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

Multiply 4 and 4 to get 16.

$$4x^{2}+4=x^{2}+16$$

Subtract x^{2} from both sides.

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

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

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

Subtract 16 from both sides.

$$3x^{2}+4-16=0$$

Subtract 16 from 4 to get -12.

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

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and -12 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-12\right)}}{2\times 3}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 3\left(-12\right)}}{2\times 3}$$

Multiply -4 times 3.

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

Multiply -12 times -12.

$$x=\frac{0±\sqrt{144}}{2\times 3}$$

Take the square root of 144.

$$x=\frac{0±12}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{0±12}{6}$$

Now solve the equation x=\frac{0±12}{6} when ± is plus. Divide 12 by 6.

$$x=2$$

Now solve the equation x=\frac{0±12}{6} when ± is minus. Divide -12 by 6.

$$x=-2$$

The equation is now solved.

$$x=2 x=-2$$