SOLUTION: Perform the indicated operation. 2/p+5 PLUS 3/p+1

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Question 117953: Perform the indicated operation.
2/p+5 PLUS 3/p+1
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
2%2F%28p%2B5%29%2B3%2F%28p%2B1%29 Start with the given expression



In order to combine these rational expressions, we need to have a common denominator
So we need to get the denominators to the LCD %28p%2B5%29%28p%2B1%29


%28%28p%2B1%29%2F%28p%2B1%29%29%282%2F%28p%2B5%29%29%2B3%2F%28p%2B1%29 Multiply the 1st term by %28%28%28p%2B1%29%29%2F%28%28p%2B1%29%29%29. This will make the 1st term have a common denominator of %28p%2B5%29%28p%2B1%29

2%28p%2B1%29%2F%28p%2B1%29%28p%2B5%29%2B3%2F%28p%2B1%29 Combine the fractions

%282p%2B2%29%2F%28p%2B1%29%28p%2B5%29%2B3%2F%28p%2B1%29 Distribute

%282p%2B2%29%2F%28p%2B1%29%28p%2B5%29%2B%28%28p%2B5%29%2F%28p%2B5%29%29%283%2F%28p%2B1%29%29 Multiply the 2nd term by %28%28%28p%2B5%29%29%2F%28%28p%2B5%29%29%29. This will make the 2nd term have a common denominator of %28p%2B5%29%28p%2B1%29


%282p%2B2%29%2F%28p%2B1%29%28p%2B5%29%2B3%28p%2B5%29%2F%28p%2B1%29%28p%2B5%29 Combine the fractions


%282p%2B2%29%2F%28p%2B1%29%28p%2B5%29%2B%283p%2B15%29%2F%28p%2B1%29%28p%2B5%29 Distribute



%28%282p%2B2%29%2B%283p%2B15%29%29%2F%28p%2B1%29%28p%2B5%29 Since every fraction has the common denominator %28p%2B5%29%28p%2B1%29, we can combine them



%285p%2B17%29%2F%28p%2B1%29%28p%2B5%29 Combine like terms



So 2%2F%28p%2B5%29%2B3%2F%28p%2B1%29 simplifies to %285p%2B17%29%2F%28p%2B1%29%28p%2B5%29