Solve x/4-1/x=5/4x

$$\frac{ x }{ 4 } - \frac{ 1 }{ x } = \frac{ 5 }{ 4x }$$

Solve for x

$$x=3$$

$$x=-3$$

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 4,x,4x.

$$xx-4=5$$

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

$$x^{2}-4=5$$

Add 4 to both sides.

$$x^{2}=5+4$$

Add 5 and 4 to get 9.

$$x^{2}=9$$

Take the square root of both sides of the equation.

$$x=3 x=-3$$

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 4,x,4x.

$$xx-4=5$$

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

$$x^{2}-4=5$$

Subtract 5 from both sides.

$$x^{2}-4-5=0$$

Subtract 5 from -4 to get -9.

$$x^{2}-9=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -9 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-9\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-9\right)}}{2}$$

Multiply -4 times -9.

$$x=\frac{0±\sqrt{36}}{2}$$

Take the square root of 36.

$$x=\frac{0±6}{2}$$

Now solve the equation x=\frac{0±6}{2} when ± is plus. Divide 6 by 2.

$$x=3$$

Now solve the equation x=\frac{0±6}{2} when ± is minus. Divide -6 by 2.

$$x=-3$$

The equation is now solved.

$$x=3 x=-3$$