Precalculus Examples

$\frac{y^{2}}{y + 5} = \frac{25}{y + 5}$

Step 1

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

$y^{2} = 25$

Step 2

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

$y = \pm \sqrt{25}$

Step 3

Simplify $\pm \sqrt{25}$ .

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Step 3.1

Rewrite $25$ as $5^{2}$ .

$y = \pm \sqrt{5^{2}}$

Step 3.2

Pull terms out from under the radical, assuming positive real numbers.

$y = \pm 5$

Step 4

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

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Step 4.1

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

$y = 5$

Step 4.2

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

$y = - 5$

Step 4.3

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

$y = 5, - 5$

Step 5

Exclude the solutions that do not make $\frac{y^{2}}{y + 5} = \frac{25}{y + 5}$ true.

$y = 5$