SOLUTION: Can you please help me with this problem? a^2-8a+12 over (like a fraction bar) 3a-18

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Question 183675: Can you please help me with this problem? a^2-8a+12 over (like a fraction bar) 3a-18
Found 2 solutions by nerdybill, jim_thompson5910:
Answer by nerdybill(5411) About Me  (Show Source):
You can put this solution on YOUR website!
%28a%5E2-8a%2B12%29%2F%283a-18%29
.
Factoring the numerator:
%28%28a-6%29%28a-2%29%29%2F%283a-18%29
.
Factoring the denominator:
%28%28a-6%29%28a-2%29%29%2F%283%28a-6%29%29
.
Notice the (a-6) cancels, leaving:
%28a-2%29%2F3

Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!

%28a%5E2-8a%2B12%29%2F%283a-18%29 Start with the given expression.


%28%28a-2%29%2A%28a-6%29%29%2F%283a-18%29 Factor a%5E2-8a%2B12 to get %28a-2%29%2A%28a-6%29.


%28%28a-2%29%2A%28a-6%29%29%2F%283%28a-6%29%29 Factor 3a-18 to get 3%28a-6%29.


%28%28a-2%29highlight%28%28a-6%29%29%29%2F%283%2Ahighlight%28%28a-6%29%29%29 Highlight the common terms.


%28%28a-2%29cross%28%28a-6%29%29%29%2F%283%2Across%28%28a-6%29%29%29 Cancel out the common terms.


%28a-2%29%2F3 Simplify.


So %28a%5E2-8a%2B12%29%2F%283a-18%29 simplifies to %28a-2%29%2F3.


In other words, %28a%5E2-8a%2B12%29%2F%283a-18%29=%28a-2%29%2F3 where a%3C%3E6