SOLUTION: Reducing rational expressions: v^2 + 3v - 18 ----------- ---- v^2 + 12v + 36

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Question 201814: Reducing rational expressions:
v^2 + 3v - 18
----------------
v^2 + 12v + 36
Found 2 solutions by Earlsdon, jim_thompson5910:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Reduce the expression:
%28v%5E2%2B3v-18%29%2F%28v%5E2%2B12v%2B36%29 Factor the numerator and the denominator.
%28%28v-3%29cross%28%28v%2B6%29%29%29%2F%28%28v%2B6%29cross%28%28v%2B6%29%29%29 Cancel the common factor (x+6)
highlight%28%28v-3%29%2F%28v%2B6%29%29

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%28v%5E2%2B3v-18%29%2F%28v%5E2%2B12v%2B36%29 Start with the given expression.


%28%28v%2B6%29%2A%28v-3%29%29%2F%28v%5E2%2B12v%2B36%29 Factor v%5E2%2B3v-18 to get %28v%2B6%29%2A%28v-3%29.


%28%28v%2B6%29%2A%28v-3%29%29%2F%28%28v%2B6%29%28v%2B6%29%29 Factor v%5E2%2B12v%2B36 to get %28v%2B6%29%28v%2B6%29.


%28highlight%28%28v%2B6%29%29%28v-3%29%29%2F%28highlight%28%28v%2B6%29%29%28v%2B6%29%29 Highlight the common terms.


%28cross%28%28v%2B6%29%29%28v-3%29%29%2F%28cross%28%28v%2B6%29%29%28v%2B6%29%29 Cancel out the common terms.


%28v-3%29%2F%28v%2B6%29 Simplify.


So %28v%5E2%2B3v-18%29%2F%28v%5E2%2B12v%2B36%29 simplifies to %28v-3%29%2F%28v%2B6%29.


In other words, %28v%5E2%2B3v-18%29%2F%28v%5E2%2B12v%2B36%29=%28v-3%29%2F%28v%2B6%29