SOLUTION: i need help with an (intermediate algerbra: Rational expressions) im not to sure how to solve it i dont what exactlt im being asked for all r is not equal to (+ or - 2. r^2 -

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: i need help with an (intermediate algerbra: Rational expressions) im not to sure how to solve it i dont what exactlt im being asked for all r is not equal to (+ or - 2. r^2 -      Log On


   

Question 254734: i need help with an (intermediate algerbra: Rational expressions)
im not to sure how to solve it i dont what exactlt im being asked
for all r is not equal to (+ or - 2.
r^2 - 5r+6
______________=?
r^2-4

a. r-3
r+2

b. r-2
r+2

c. r-2
r+3

d. r+3
r-2

e. r+3
r+2

i need to know how to do it to get the correct answer i have a test at ecpi on saturday i can figure out how to work it out to get the answer they want please and thank you
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