# How do you simplify (p+4)/(p^2+6p+8)?

Apr 17, 2018

$= \left(\frac{1}{p + 2}\right)$

#### Explanation:

$\frac{p + 4}{{p}^{2} + 6 p + 8}$
$= \frac{p + 4}{\left(p + 2\right) \left(p + 4\right)}$
$= \left(\frac{1}{p + 2}\right)$

Apr 17, 2018

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

#### Explanation:

Step A: $\setminus \boldsymbol{\setminus \textrm{S i m p l \mathmr{if} y t h e \mathrm{de} n o \min a \to r .}}$

1. It's in the form "$a {p}^{2} + b p + c$," which means your factors ${p}_{1}$ and ${p}_{2}$ must add to be $b$ and multiply to be $a \setminus \cdot c$.
In other words: $\setminus \boldsymbol{{p}_{1} + {p}_{2} = b}$ and $\setminus \boldsymbol{{p}_{1} \left({p}_{2}\right) = a \setminus \cdot c}$

2. $a = 1$, $b = 6$, $c = 8$; so ${p}_{1} + {p}_{2} = 6$ and ${p}_{1} \left({p}_{2}\right) = 1 \setminus \cdot 8 = 8$
The only two factors that fulfill these requirements are $\setminus \boldsymbol{2}$ and $\setminus \boldsymbol{4}$. Which means you can factor the polynomial ${p}^{2} + 6 p + 8$ to $\left(p + 2\right) \left(p + 4\right)$.

3. Your new expression is $\frac{p + 4}{\left(p + 2\right) \left(p + 4\right)}$.
See anything you can cross out?

Step B: $\setminus \boldsymbol{\setminus \textrm{I \mathrm{de} n t \mathmr{if} y s i m i l a r t e r m s \to \cancel{.}}}$

1. We see that $p + 4$ occurs twice, one in the numerator, and one in the denominator.
(\color(red)(p+4))/((p+2)(\color(red)(p+4))

2. You can cancel out similar terms, so we cross out those two.
\cancel(\color(red)(p+4))/((p+2)(\cancel(\color(red)(p+4)))

3. Remove the crossed out parts...
$\frac{1}{\left(p + 2\right) \left(1\right)}$

Step C: \text(Remove the 1s, and)\bb(\text( you have your answer!))
$\frac{1}{p + 2}$