SOLUTION: I have to perform the operation of: <pre> k^2+3k-10 3 _________ x ________ 36 k^2-4 </pre> I tried to look for simplification by factoring out the first

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I have to perform the operation of: <pre> k^2+3k-10 3 _________ x ________ 36 k^2-4 </pre> I tried to look for simplification by factoring out the first      Log On


   

Question 203062: I have to perform the operation of: 

k^2+3k-10      3
_________ x ________
    36       k^2-4

I tried to look for simplification by factoring out the first numerator to (k+5)(k-2). But I don't see how I can factor out a (k-2) from the second denominator because there's no k value in the expression. However, the choices for answers indicate that it is cancelled out somehow. Where do I go from here?
Found 2 solutions by Earlsdon, jim_thompson5910:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
It would help if you were to use paretheses to clarify the problem, eg:
((k^2+3k-10)/(36))*(3/(k^2-4)) I hope I've got this right!
%28%28k%5E2%2B3k-10%29%2F36%29%2A%283%2F%28k%5E2-4%29%29 Factor the first numerator and denominator and factor the second denominator.
Cancel the common factors as shown to leave you with:
highlight%28%28k%2B5%29%2F%2812%2A%28k%2B2%29%29%29 or highlight_green%28%28k%2B5%29%2F%2812k%2B24%29%29

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28%28k%5E2%2B3k-10%29%2F36%29%283%2F%28k%5E2-4%29%29 Start with the given expression.


%28%28%28k%2B5%29%28k-2%29%29%2F36%29%283%2F%28k%5E2-4%29%29 Factor the first numerator


%28%28%28k%2B5%29%28k-2%29%29%2F%2812%2A3%29%29%283%2F%28k%5E2-4%29%29 Factor the first denominator


%28%28%28k%2B5%29%28k-2%29%29%2F%2812%2A3%29%29%283%2F%28%28k-2%29%28k%2B2%29%29%29 Factor the second denominator (hint: use the difference of squares formula)


%283%28k%2B5%29%28k-2%29%29%2F%2812%2A3%28k-2%29%28k%2B2%29%29 Combine the fractions.


Highlight the common terms.


Cancel out the common terms.


%28k%2B5%29%2F%2812%28k%2B2%29%29 Simplify


%28k%2B5%29%2F%2812k%2B24%29 Distribute



So %28%28k%5E2%2B3k-10%29%2F36%29%283%2F%28k%5E2-4%29%29 simplifies to %28k%2B5%29%2F%2812k%2B24%29


In other words, %28%28k%5E2%2B3k-10%29%2F36%29%283%2F%28k%5E2-4%29%29=%28k%2B5%29%2F%2812k%2B24%29