# How do you combine (x^2) / (x+5) - (25 )/ (x+5)?

May 19, 2015

When you have the sum/subtraction of fractions that share the same denominator, you simply add/subtract the numerators:

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

However, we can factorate ${x}^{2} - 25$ by equaling it to zero and finding its roots:

${x}^{2} - 25 = 0$
${x}^{2} = 25$
$x = \sqrt{25}$
${x}_{1} = 5$, which is the same as the factor $\left(x - 5\right) = 0$
${x}_{2} = - 5$, which is the same as the factor $\left(x + 5\right) = 0$

Now, rewriting,

$\frac{\cancel{x + 5} \left(x - 5\right)}{\cancel{x + 5}}$

Your final answer, then, is $\left(x - 5\right)$