SOLUTION: complex rational expressions: 5 _____ -5 3r-1 ___________ _ 5 ______ +5 3r-1

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Question 198575: complex rational expressions:
5
_____ -5
3r-1
_____________
5
______ +5
3r-1
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%285%2F%283r-1%29-5%29%2F%285%2F%283r-1%29%2B5%29 Start with the given expression.


Multiply EVERY term by the inner LCD 3r-1 to clear out the inner fractions.


%285-5%283r-1%29%29%2F%285%2B5%283r-1%29%29 Simplify


%285-15r%2B5%29%2F%285%2B15r-5%29 Distribute


%2810-15r%29%2F%2815r%29 Combine like terms.


%285%282-3r%29%29%2F%2815r%29 Factor the numerator


%285%282-3r%29%29%2F%285%2A3r%29 Factor the denominator


%28cross%285%29%282-3r%29%29%2F%28cross%285%29%2A3r%29 Cancel out the common terms.


%282-3r%29%2F%283r%29 Simplify


So %285%2F%283r-1%29-5%29%2F%285%2F%283r-1%29%2B5%29=%282-3r%29%2F%283r%29