Solve for y 1-y^2=y^2-1

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

Step 1

Move all terms containing $y$ to the left side of the equation.

Subtract $y^{2}$ from both sides of the equation.

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

Subtract $y^{2}$ from $- y^{2}$ .

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

Step 2

Move all terms not containing $y$ to the right side of the equation.

Subtract $1$ from both sides of the equation.

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

Subtract $1$ from $- 1$ .

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

Step 3

Divide each term in $- 2 y^{2} = - 2$ by $- 2$ and simplify.

Divide each term in $- 2 y^{2} = - 2$ by $- 2$ .

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

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

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

Divide $y^{2}$ by $1$ .

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

Simplify the right side.

Divide $- 2$ by $- 2$ .

$y^{2} = 1$

Step 4

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$y = \pm \sqrt{1}$

Step 5

Any root of $1$ is $1$ .

$y = \pm 1$

Step 6

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$y = 1$

Next, use the negative value of the $\pm$ to find the second solution.

$y = - 1$

The complete solution is the result of both the positive and negative portions of the solution.

$y = 1, - 1$