SOLUTION: I really need your help in solving this problem. I appreciate your time and efforts. Have a terrific day :) Here is the question? Simplify: y^2 -25/y^2 -3y-10

Algebra ->  Rational-functions -> SOLUTION: I really need your help in solving this problem. I appreciate your time and efforts. Have a terrific day :) Here is the question? Simplify: y^2 -25/y^2 -3y-10       Log On


   

Question 916854: I really need your help in solving this problem. I appreciate your time and efforts. Have a terrific day :) Here is the question? Simplify:
y^2 -25/y^2 -3y-10
Found 3 solutions by jim_thompson5910, Hawksfan, DrBeeee:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Factor each as much as possible. Then cancel out any similar terms.

%28y%5E2+-25%29%2F%28y%5E2+-3y-10+%29

%28y%5E2+-5%5E2%29%2F%28y%5E2+-3y-10+%29

%28%28y-5%29%28y%2B5%29%29%2F%28y%5E2+-3y-10+%29

%28%28y-5%29%28y%2B5%29%29%2F%28%28y-5%29%28y%2B2%29%29

%28highlight%28%28y-5%29%29%28y%2B5%29%29%2F%28highlight%28%28y-5%29%29%28y%2B2%29%29

%28cross%28%28y-5%29%29%28y%2B5%29%29%2F%28cross%28%28y-5%29%29%28y%2B2%29%29

%28y%2B5%29%2F%28y%2B2%29

-------------------------------------------------------

So %28y%5E2+-25%29%2F%28y%5E2+-3y-10+%29 fully simplifies to %28y%2B5%29%2F%28y%2B2%29

Let me know if you need more help or if you need me to explain a step in more detail.
Feel free to email me at jim_thompson5910@hotmail.com
or you can visit my website here: http://www.freewebs.com/jimthompson5910/home.html

Thanks,

Jim

Answer by Hawksfan(61) About Me  (Show Source):
You can put this solution on YOUR website!
y^2 -25/y^2 -3y-10
factor both the numerator and the denominator
the numerator is a difference of two squares of the form x^2 - y^2 = (x-y)(x+y)
(y-5)(y+5)/(y-5)(y+2) =
What's in common? y-5
Divide out y-5
= (y+5)/(y+2)

Answer by DrBeeee(684) About Me  (Show Source):
You can put this solution on YOUR website!
Given:
(1) y^2 -25/y^2 -3y-10
But I think you mean
(2) (y^2 -25)/(y^2 -3y-10), which makes all the difference in the world!
In (2) you can factor the numerator
(3) y^2 -25 = (y-5)*(y+5) and the denominator
(4) y^2 -3y-10 = (y-5)*(y+2)
Now place (3) and (4) into (2) to get
(5)(y^2 -25)/(y^2 -3y-10) = ((y-5)*(y+5))/((y-5)*(y+2)) or after cancellation of (y-5) we get
(6)(y^2 -25)/(y^2 -3y-10) = (y+5)/(y+2)
Answer: The given expression simplifies to (y+5)/(y+2).