SOLUTION: it says for all r, then has an = sign with a line thru it, +_ 2. so not equall to and plus or minus to 2? r^2-5r+6 over r^2-4. answer is r-3 over r+2. not sure how to get this answ

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: it says for all r, then has an = sign with a line thru it, +_ 2. so not equall to and plus or minus to 2? r^2-5r+6 over r^2-4. answer is r-3 over r+2. not sure how to get this answ      Log On


   

Question 253943: it says for all r, then has an = sign with a line thru it, +_ 2. so not equall to and plus or minus to 2? r^2-5r+6 over r^2-4. answer is r-3 over r+2. not sure how to get this answer. Thanks!
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
The key to this problem is factoring.


%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 (note: if you need help with factoring, check out this solver)


%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

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
it says for all r, then has an = sign with a line thru it, +_ 2. so not equall to and plus or minus to 2?
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For all r not equal to +/-2
(r^2-5r+6)/(r^2-4)
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= [(r-3)(r-2)]/[(r-2)(r+2)]
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= (r-3)/(r+2)
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Cheers,
Stan H.