Solve y=1/y

$$y= \frac{ 1 }{ y }$$

Solve for y

$$y=1$$

$$y=-1$$

Steps Using Difference of Squares

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

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

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

$$\frac{yy}{y}-\frac{1}{y}=0$$

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

$$\frac{yy-1}{y}=0$$

Do the multiplications in yy-1.

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

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

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

Consider y^{2}-1. Rewrite y^{2}-1 as y^{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).

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

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

$$y=1 y=-1$$

Steps by Finding Square Root

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

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

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

$$\frac{yy}{y}-\frac{1}{y}=0$$

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

$$\frac{yy-1}{y}=0$$

Do the multiplications in yy-1.

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

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

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

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

$$y^{2}=1$$

Take the square root of both sides of the equation.

$$y=1 y=-1$$

Steps Using the Quadratic Formula

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

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

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

$$\frac{yy}{y}-\frac{1}{y}=0$$

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

$$\frac{yy-1}{y}=0$$

Do the multiplications in yy-1.

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

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

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

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}.

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

Square 0.

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

Multiply -4 times -1.

$$y=\frac{0±\sqrt{4}}{2}$$

Take the square root of 4.

$$y=\frac{0±2}{2}$$

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

$$y=1$$

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

$$y=-1$$

The equation is now solved.

$$y=1 y=-1$$