Solve 3/x=1/x^2quad4/2x

$$\frac { 3 } { x } = \frac { 1 } { x ^ { 2 } } \quad \frac { 4 } { 2 x }$$

Solve for x

$$x=\frac{\sqrt{6}}{3}\approx 0.816496581$$

$$x=-\frac{\sqrt{6}}{3}\approx -0.816496581$$

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 2x^{2}, the least common multiple of x,x^{2},2x.

$$2x\times 3=2\times 1\times \frac{4}{2x}$$

Multiply 2 and 3 to get 6.

$$6x=2\times 1\times \frac{4}{2x}$$

Multiply 2 and 1 to get 2.

$$6x=2\times \frac{4}{2x}$$

Express 2\times \frac{4}{2x} as a single fraction.

$$6x=\frac{2\times 4}{2x}$$

Cancel out 2 in both numerator and denominator.

$$6x=\frac{4}{x}$$

Subtract \frac{4}{x} from both sides.

$$6x-\frac{4}{x}=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 6x times \frac{x}{x}.

$$\frac{6xx}{x}-\frac{4}{x}=0$$

Since \frac{6xx}{x} and \frac{4}{x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6xx-4}{x}=0$$

Do the multiplications in 6xx-4.

$$\frac{6x^{2}-4}{x}=0$$

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$6x^{2}-4=0$$

Add 4 to both sides. Anything plus zero gives itself.

$$6x^{2}=4$$

Divide both sides by 6.

$$x^{2}=\frac{4}{6}$$

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

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

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{6}}{3} x=-\frac{\sqrt{6}}{3}$$

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 2x^{2}, the least common multiple of x,x^{2},2x.

$$2x\times 3=2\times 1\times \frac{4}{2x}$$

Multiply 2 and 3 to get 6.

$$6x=2\times 1\times \frac{4}{2x}$$

Multiply 2 and 1 to get 2.

$$6x=2\times \frac{4}{2x}$$

Express 2\times \frac{4}{2x} as a single fraction.

$$6x=\frac{2\times 4}{2x}$$

Cancel out 2 in both numerator and denominator.

$$6x=\frac{4}{x}$$

Subtract \frac{4}{x} from both sides.

$$6x-\frac{4}{x}=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 6x times \frac{x}{x}.

$$\frac{6xx}{x}-\frac{4}{x}=0$$

Since \frac{6xx}{x} and \frac{4}{x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6xx-4}{x}=0$$

Do the multiplications in 6xx-4.

$$\frac{6x^{2}-4}{x}=0$$

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$6x^{2}-4=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 6 for a, 0 for b, and -4 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 6\left(-4\right)}}{2\times 6}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 6\left(-4\right)}}{2\times 6}$$

Multiply -4 times 6.

$$x=\frac{0±\sqrt{-24\left(-4\right)}}{2\times 6}$$

Multiply -24 times -4.

$$x=\frac{0±\sqrt{96}}{2\times 6}$$

Take the square root of 96.

$$x=\frac{0±4\sqrt{6}}{2\times 6}$$

Multiply 2 times 6.

$$x=\frac{0±4\sqrt{6}}{12}$$

Now solve the equation x=\frac{0±4\sqrt{6}}{12} when ± is plus.

$$x=\frac{\sqrt{6}}{3}$$

Now solve the equation x=\frac{0±4\sqrt{6}}{12} when ± is minus.

$$x=-\frac{\sqrt{6}}{3}$$

The equation is now solved.

$$x=\frac{\sqrt{6}}{3} x=-\frac{\sqrt{6}}{3}$$