Solve for y (y^2)/(y+1)=1/(y+1)

$\frac{y^{2}}{y + 1} = \frac{1}{y + 1}$

Step 1

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$y^{2} = 1$

Step 2

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

$y = \pm \sqrt{1}$

Step 3

Any root of $1$ is $1$ .

$y = \pm 1$

Step 4

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.

$y = 1, - 1$

Step 5

Exclude the solutions that do not make $\frac{y^{2}}{y + 1} = \frac{1}{y + 1}$ true.

$y = 1$