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

2 Answers
Apr 17, 2018

= (1/(p+2))

Explanation:

(p + 4) / (p^2 + 6p + 8)
= (p+4)/((p+2)(p+4))
= (1/(p+2))

Apr 17, 2018

1/(p+2)

Explanation:

Step A: \bb(\text(Simplify the denominator.))

  1. It's in the form "ap^2+bp+c," which means your factors p_1 and p_2 must add to be b and multiply to be a\cdotc.
    In other words: \bb(p_1+p_2=b) and \bb(p_1(p_2)=a\cdotc)

  2. a=1, b=6, c=8; so p_1+p_2=6 and p_1(p_2)=1\cdot8=8
    The only two factors that fulfill these requirements are \bb2 and \bb4. Which means you can factor the polynomial p^2+6p+8 to (p+2)(p+4).

  3. Your new expression is (p+4)/((p+2)(p+4)).
    See anything you can cross out?

Step B: \bb(\text(Identify similar terms 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...
    1/((p+2)(1))

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