# How do you simplify (x+5)/(x^2+7x+10)?

$\frac{1}{x + 2}$

#### Explanation:

Given that

$\setminus \frac{x + 5}{{x}^{2} + 7 x + 10}$

$= \setminus \frac{x + 5}{{x}^{2} + 5 x + 2 x + 10}$

$= \setminus \frac{x + 5}{x \left(x + 5\right) + 2 \left(x + 5\right)}$

$= \setminus \frac{x + 5}{\left(x + 5\right) \left(x + 2\right)}$

$= \frac{1}{x + 2}$

Jul 9, 2018

$\frac{1}{x + 2}$

#### Explanation:

Let's see if we can factor the denominator first. What two numbers sum up to the middle term and have a product of the last term?

After some trial and error, we arrive at $5$ and $2$, which means we can factor the denominator as

$\left(x + 5\right) \left(x + 2\right)$

We now have the following expression

$\frac{x + 5}{\left(x + 2\right) \left(x + 5\right)}$

Same terms on the top and bottom cancel, and we're left with

$\frac{\cancel{x + 5}}{\left(x + 2\right) \cancel{x + 5}}$

$\frac{1}{x + 2}$

Hope this helps!