SOLUTION: This problem isn't from a textbook. It's from a practice booklet for a placement test I have to take. For all r does not = +/- 2, r squared - 5r + 6 / r squared - 4 = ?

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: This problem isn't from a textbook. It's from a practice booklet for a placement test I have to take. For all r does not = +/- 2, r squared - 5r + 6 / r squared - 4 = ?      Log On


   

Question 145843: This problem isn't from a textbook. It's from a practice booklet for a placement test I have to take.
For all r does not = +/- 2, r squared - 5r + 6 / r squared - 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%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