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OpenStudy (anonymous):
jimthompson5910 (jim_thompson5910):
Can you factor the numerator and denominator at all?
OpenStudy (anonymous):
what do u mean
jimthompson5910 (jim_thompson5910):
What does x^2+5x+6 factor to
OpenStudy (anonymous):
i dont know im really confused in these algebra questions
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jimthompson5910 (jim_thompson5910):
Notice how 2 and 3 multiply to 6 and add to 5
So x^2+5x+6 factors to (x+2)(x+3)
jimthompson5910 (jim_thompson5910):
What about the denominator
OpenStudy (anonymous):
Yes, you can simplify this.
\[\frac{x^2+5x+6}{x^2+x-2}=\frac{(x+3)(x+2)}{(x-1)(x+2)}\]
After factoring. Thus, we get, after cancelling
\[\frac{(x+3)}{(x-1)}, x\neq-2\]
OpenStudy (anonymous):
x^2+x-2 is the bottom part of the fraction
jimthompson5910 (jim_thompson5910):
yes, can that be factored? if so, what does it factor to?
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OpenStudy (anonymous):
yes
OpenStudy (anonymous):
(x+2)(x+2)
jimthompson5910 (jim_thompson5910):
not quite
jimthompson5910 (jim_thompson5910):
Find two numbers that multiply to -2 and add to 1
OpenStudy (anonymous):
wow this is hard
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jimthompson5910 (jim_thompson5910):
it will get easier with more practice
OpenStudy (anonymous):
-2*1=-2
jimthompson5910 (jim_thompson5910):
close, more like 2*(-1) = -2 and 2 + (-1) = 1
So it factors to (x+2)(x-1)
OpenStudy (anonymous):
oh
jimthompson5910 (jim_thompson5910):
You'll notice there's a 'x+2' up top and a 'x+2' in the bottom, they cancel and go away
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OpenStudy (anonymous):
ok
OpenStudy (anonymous):
|dw:1346551722615:dw|so ill stay with
jimthompson5910 (jim_thompson5910):
yes
jimthompson5910 (jim_thompson5910):
you can erase the parenthesis if you want since they're not doing anything
jimthompson5910 (jim_thompson5910):
so that means choice D is your answer
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