SOLUTION: Intermediate Algebra: Rational Expressions For all r≠ ± 2, r^2 - 5r + 6 / r^2 - 4 = ? Can you give me a really detailed explanation of how you get the answer? Thanks!

Algebra ->  Algebra  -> Rational-functions -> SOLUTION: Intermediate Algebra: Rational Expressions For all r≠ ± 2, r^2 - 5r + 6 / r^2 - 4 = ? Can you give me a really detailed explanation of how you get the answer? Thanks!      Log On

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Question 145697: Intermediate Algebra: Rational Expressions
For all r≠ ± 2, r^2 - 5r + 6 / r^2 - 4 = ?
Can you give me a really detailed explanation of how you get the answer? Thanks!
Answer by jim_thompson5910(21685) 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%2A%28r-3%29%29%2F%28r%5E2-4%29 Factor r%5E2-5r%2B6 to get %28r-2%29%2A%28r-3%29.


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


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


%28cross%28r-2%29%28r-3%29%29%2F%28cross%28r-2%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