SOLUTION: For all r not equal to + or - 2, r^2-5r+6/r^2-4

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Question 153225: For all r not equal to + or - 2, r^2-5r+6/r^2-4
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%28r%5E2-5r%2B6%29%2F%28r%5E2-4%29 Start with the given expression.


%28%28r-2%29%28r-3%29%29%2F%28r%5E2-4%29 Factor r%5E2-5r%2B6 to get %28r-2%29%28r-3%29.


%28%28r-2%29%28r-3%29%29%2F%28%28r-2%29%28r%2B2%29%29 Factor r%5E2-4 to get %28r-2%29%28r%2B2%29.


%28highlight%28%28r-2%29%29%28r-3%29%29%2F%28highlight%28%28r-2%29%29%28r%2B2%29%29 Highlight the common terms.


%28cross%28%28r-2%29%29%28r-3%29%29%2F%28cross%28%28r-2%29%29%28r%2B2%29%29 Cancel out the common terms.


%28r-3%29%2F%28r%2B2%29 Simplify.


So %28r%5E2-5r%2B6%29%2F%28r%5E2-4%29 simplifies to %28r-3%29%2F%28r%2B2%29.


In other words, %28r%5E2-5r%2B6%29%2F%28r%5E2-4%29=%28r-3%29%2F%28r%2B2%29 where r%3C%3E-2 or r%3C%3E2