SOLUTION: subtract and simply a - c ------- ---------- ac-c2 - a2-ac c2 is c squared and a2 is a squared thank you

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Question 149914: subtract and simply

a - c
------- ----------
ac-c2 - a2-ac

c2 is c squared and a2 is a squared
thank you
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28a%29%2F%28ac-c%5E2%29-%28c%29%2F%28a%5E2-ac%29 Start with the given expression.


%28a%29%2F%28c%28a-c%29%29-%28c%29%2F%28a%5E2-ac%29 Factor ac-c%5E2 to get c%28a-c%29


%28a%29%2F%28c%28a-c%29%29-%28c%29%2F%28a%28a-c%29%29 Factor a%5E2-ac to get a%28a-c%29


Notice how the LCD is ac%28a-c%29


%28a%2Fa%29%28%28a%29%2F%28c%28a-c%29%29%29-%28c%29%2F%28a%28a-c%29%29 Multiply the first fraction by a%2Fa. This will make the first fraction have a denominator of ac%28a-c%29


%28a%5E2%29%2F%28ac%28a-c%29%29-%28c%29%2F%28a%28a-c%29%29 Combine the fractions and multiply.


%28a%5E2%29%2F%28ac%28a-c%29%29-%28c%2Fc%29%28%28c%29%2F%28a%28a-c%29%29%29 Multiply the second fraction by c%2Fc. This will make the second fraction have a denominator of ac%28a-c%29


%28a%5E2%29%2F%28ac%28a-c%29%29-%28c%5E2%29%2F%28ac%28a-c%29%29 Combine the fractions and multiply.


Since the denominators are now equal, this means that we can combine the fractions.

%28a%5E2-c%5E2%29%2F%28ac%28a-c%29%29 Combine the numerators over the common denominator.


%28%28a%2Bc%29%28a-c%29%29%2F%28ac%28a-c%29%29 Factor a%5E2-c%5E2 to get %28a%2Bc%29%28a-c%29


%28%28a%2Bc%29highlight%28%28a-c%29%29%29%2F%28ac%2Ahighlight%28%28a-c%29%29%29 Highlight the common terms.


%28%28a%2Bc%29cross%28%28a-c%29%29%29%2F%28ac%2Across%28%28a-c%29%29%29 Cancel out the common terms.


%28a%2Bc%29%2F%28ac%29 Simplify


So %28a%29%2F%28ac-c%5E2%29-%28c%29%2F%28a%5E2-ac%29 simplifies to %28a%2Bc%29%2F%28ac%29.