SOLUTION: Divide the following fractions. 6p-18 3p-9 ----- divided by ------ 9p p^2+2p

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Divide the following fractions. 6p-18 3p-9 ----- divided by ------ 9p p^2+2p      Log On


   

Question 117935: Divide the following fractions.
6p-18 3p-9
----- divided by ------
9p p^2+2p
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28%286p-18%29%2F%289p%29%29%2F%28%283p-9%29%2F%28p%5E2%2B2p%29%29 Start with the given expression

%28%286p-18%29%2F%289p%29%29%2A%28%28%28p%5E2%2B2p%29%29%2F%28%283p-9%29%29%29 Multiply the first fraction by the reciprocal of the second fraction


%28%286%28p-3%29%29%2F%289p%29%29%28%28p%5E2%2B2p%29%2F%283p-9%29%29 Factor 6p-18 to get 6%28p-3%29

%28%286%28p-3%29%29%2F%289%28p%29%29%29%28%28p%5E2%2B2p%29%2F%283p-9%29%29 Factor 9p to get 9%28p%29

%28%286%28p-3%29%29%2F%289%28p%29%29%29%28%28p%28p%2B2%29%29%2F%283p-9%29%29 Factor p%5E2%2B2p to get p%28p%2B2%29

%28%286%28p-3%29%29%2F%289%28p%29%29%29%28%28p%28p%2B2%29%29%2F%283%28p-3%29%29%29 Factor 3p-9 to get 3%28p-3%29

%28%28%282%2A3%29%28p-3%29%29%2F%289%28p%29%29%29%28%28p%28p%2B2%29%29%2F%283%28p-3%29%29%29 Factor 6 into 2*3


%282%2A3%29%28p-3%29p%28p%2B2%29%2F9%28p%293%28p-3%29 Combine the fractions


Cancel like terms


2%28p%2B2%29%2F9 Simplify


So %28%286p-18%29%2F%289p%29%29%2F%28%283p-9%29%2F%28p%5E2%2B2p%29%29 simplifies to 2%28p%2B2%29%2F9.


Note: This is not a typo even though this answer is identical to the previous one. The previous expression %28%286p-18%29%2F%283p-9%29%29%2F%28%289p%29%2F%28p%5E2%2B2p%29%29 is the same as %28%286p-18%29%2F%289p%29%29%2F%28%283p-9%29%2F%28p%5E2%2B2p%29%29. Can you see why?

%28%286p-18%29%2F%283p-9%29%29%2F%28%289p%29%2F%28p%5E2%2B2p%29%29 ---> %28%286p-18%29%2F%283p-9%29%29%2A%28%28%28p%5E2%2B2p%29%29%2F%28%289p%29%29%29 and

%28%286p-18%29%2F%289p%29%29%2F%28%283p-9%29%2F%28p%5E2%2B2p%29%29 ---> %28%286p-18%29%2F%289p%29%29%2A%28%28%28p%5E2%2B2p%29%29%2F%28%283p-9%29%29%29


For each second expression, notice the denominators have swapped. Since they all get combined in one big denominator, the answer does not change.