Answer
To check our answers, we plug the values into the original equation. Let's check $x = -5$ first:
$\frac{{-5}^2}{-5 + 5} = \frac{25}{-5 + 5}$
Simplify the denominator:
$\frac{{-5}^2}{0} = \frac{25}{0}$
The fractions are undefined; therefore, we cannot use this solution.
Let's check $x = 5$:
$\frac{{5}^2}{5 + 5} = \frac{25}{5 + 5}$
Simplify the denominator:
$\frac{{-5}^2}{10} = \frac{25}{10}$
Simplify the numerator:
$\frac{25}{10} = \frac{25}{10}$
The two sides are equal to one another. The correct solution is $x = 5$.
Work Step by Step
The first thing we want to do is get rid of the fractions. We do this by first finding the least common denominator (LCD) for all the terms.
We find the LCD by taking the highest power of each factor in the denominators of the fractions:
LCD = $x + 5$
Now, we will multiply each numerator by the factor its denominator is missing from the LCD:
$25(x + 5) = x^2(x + 5)$
We can cancel out the $x + 5$ from both sides of the equation:
$x^2 = 25$
Take the square root of both sides:
$x = ±5$
The solution is $x = ±5$.
