Solve 4+k/4=k+4/k

$$\frac { 4 + k } { 4 } = \frac { k + 4 } { k }$$

Solve for k

$$k=-4$$

$$k=4$$

Steps by Finding Square Root

Variable k cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 4k, the least common multiple of 4,k.

$$k\left(4+k\right)=4\left(k+4\right)$$

Use the distributive property to multiply k by 4+k.

$$4k+k^{2}=4\left(k+4\right)$$

Use the distributive property to multiply 4 by k+4.

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

Subtract 4k from both sides.

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

Combine 4k and -4k to get 0.

$$k^{2}=16$$

Take the square root of both sides of the equation.

$$k=4 k=-4$$

Steps Using the Quadratic Formula

Variable k cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 4k, the least common multiple of 4,k.

$$k\left(4+k\right)=4\left(k+4\right)$$

Use the distributive property to multiply k by 4+k.

$$4k+k^{2}=4\left(k+4\right)$$

Use the distributive property to multiply 4 by k+4.

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

Subtract 4k from both sides.

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

Combine 4k and -4k to get 0.

$$k^{2}=16$$

Subtract 16 from both sides.

$$k^{2}-16=0$$

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}.

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

Square 0.

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

Multiply -4 times -16.

$$k=\frac{0±\sqrt{64}}{2}$$

Take the square root of 64.

$$k=\frac{0±8}{2}$$

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

$$k=4$$

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

$$k=-4$$

The equation is now solved.

$$k=4 k=-4$$