SOLUTION: What are the steps for this problem: Add: 2/x + 1/x+4

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Question 118796: What are the steps for this problem:
Add: 2/x + 1/x+4
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%282%29%2F%28x%29%2B%281%29%2F%28x%2B4%29 Start with the given expression




Since the denominators are not equal, we need to get them to a common denominator. Since the LCD is %28x%29%28x%2B4%29, we need to get each denominator to %28x%29%28x%2B4%29




%28%28%28x%2B4%29%29%2F%28%28x%2B4%29%29%29%28%282%29%2F%28x%29%29%2B%281%29%2F%28x%2B4%29 Multiply %282%29%2F%28x%29 by %28%28x%2B4%29%29%2F%28%28x%2B4%29%29



%28x%2B4%29%282%29%2F%28%28x%29%28x%2B4%29%29%2B%281%29%2F%28x%2B4%29 Combine the fractions



%282x%2B8%29%2F%28%28x%29%28x%2B4%29%29%2B%281%29%2F%28x%2B4%29 Distribute



Multiply %281%29%2F%28x%2B4%29 by %28%28x%29%29%2F%28%28x%29%29



%282x%2B8%29%2F%28%28x%29%28x%2B4%29%29%2B%28x%29%281%29%2F%28%28x%29%28x%2B4%29%29 Combine the fractions



%282x%2B8%29%2F%28%28x%29%28x%2B4%29%29%2B%28x%29%2F%28%28x%29%28x%2B4%29%29 Multiply



%282x%2B8%2Bx%29%2F%28x%29%28x%2B4%29 Since the 2 fractions have the common denominator %28x%29%28x%2B4%29, we can combine them. In order to do that, just combine the numerators.


%283x%2B8%29%2F%28x%29%28x%2B4%29 Combine like terms



So %282%29%2F%28x%29%2B%281%29%2F%28x%2B4%29 simplifies to %283x%2B8%29%2F%28x%29%28x%2B4%29


In other words, %282%29%2F%28x%29%2B%281%29%2F%28x%2B4%29=%283x%2B8%29%2F%28x%29%28x%2B4%29