Solve x%=x/x^2%

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

Solve for x

$$x=1$$

$$x=-1$$

Steps Using Difference of Squares

Multiply both sides of the equation by 100.

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

Rewrite x^{2} as xx. Cancel out x in both numerator and denominator.

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

Subtract \frac{1}{x} from both sides.

$$x-\frac{1}{x}=0$$

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

$$\frac{xx}{x}-\frac{1}{x}=0$$

Since \frac{xx}{x} and \frac{1}{x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{xx-1}{x}=0$$

Do the multiplications in xx-1.

$$\frac{x^{2}-1}{x}=0$$

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

$$x^{2}-1=0$$

Consider x^{2}-1. Rewrite x^{2}-1 as x^{2}-1^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-1\right)\left(x+1\right)=0$$

To find equation solutions, solve x-1=0 and x+1=0.

$$x=1 x=-1$$

Steps by Finding Square Root

Multiply both sides of the equation by 100.

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

Rewrite x^{2} as xx. Cancel out x in both numerator and denominator.

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

Subtract \frac{1}{x} from both sides.

$$x-\frac{1}{x}=0$$

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

$$\frac{xx}{x}-\frac{1}{x}=0$$

Since \frac{xx}{x} and \frac{1}{x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{xx-1}{x}=0$$

Do the multiplications in xx-1.

$$\frac{x^{2}-1}{x}=0$$

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

$$x^{2}-1=0$$

Add 1 to both sides. Anything plus zero gives itself.

$$x^{2}=1$$

Take the square root of both sides of the equation.

$$x=1 x=-1$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 100.

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

Rewrite x^{2} as xx. Cancel out x in both numerator and denominator.

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

Subtract \frac{1}{x} from both sides.

$$x-\frac{1}{x}=0$$

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

$$\frac{xx}{x}-\frac{1}{x}=0$$

Since \frac{xx}{x} and \frac{1}{x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{xx-1}{x}=0$$

Do the multiplications in xx-1.

$$\frac{x^{2}-1}{x}=0$$

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

$$x^{2}-1=0$$

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

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1\right)}}{2}$$

Multiply -4 times -1.

$$x=\frac{0±\sqrt{4}}{2}$$

Take the square root of 4.

$$x=\frac{0±2}{2}$$

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

$$x=1$$

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

$$x=-1$$

The equation is now solved.

$$x=1 x=-1$$