Solve for x (x^2)/(x+5)=25/(x+5)

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

Step 1

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

$x^{2} = 25$

Step 2

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

$x = \pm \sqrt{25}$

Step 3

Simplify $\pm \sqrt{25}$ .

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

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

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

$x = \pm 5$

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.

$x = 5$

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

$x = - 5$

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

$x = 5, - 5$

Step 5

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

$x = 5$