How do you simplify (p+4)/(p^2+6p+8)?
2 Answers
Explanation:
Explanation:
Step A:
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It's in the form "
ap^2+bp+c ," which means your factorsp_1 andp_2 must add to beb and multiply to bea\cdotc .
In other words:\bb(p_1+p_2=b) and\bb(p_1(p_2)=a\cdotc) -
a=1 ,b=6 ,c=8 ; sop_1+p_2=6 andp_1(p_2)=1\cdot8=8
The only two factors that fulfill these requirements are\bb2 and\bb4 . Which means you can factor the polynomialp^2+6p+8 to(p+2)(p+4) . -
Your new expression is
(p+4)/((p+2)(p+4)) .
See anything you can cross out?
Step B:
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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)) -
You can cancel out similar terms, so we cross out those two.
\cancel(\color(red)(p+4))/((p+2)(\cancel(\color(red)(p+4))) -
Remove the crossed out parts...
1/((p+2)(1))
Step C: