Can someone show me how do i multiply the following fractions:
(n^2-n-20)/(2n^2) times (n^2+5n)/(n^2-25)
When you multiply fractions, you just multiply straight across. So if you have:
1/3 * 1/4
1*1
----
3*4
That's 1/12
With that in mind, let's look at your question:
(n^2-n-20)(n^2+5n)
-------------------
(2n^2)(n^2-25)
Let's start off, to make it possibly a little easier, by factoring out what we can:
(n^2-n-20) can be written:
(n-5)(n+4)
So now we have
(n-5)(n+4)(n^2+5n)
------------------
(2n^2)(n^2-25)
The n^2+5n can be:
n(n+5)
Phew. So...all together on top, we have
(n-5)(n+4)(n)(n+5)
Now, the bottom.
2n^2 can be left alone.
n^2-25 can be:
(n-5)(n+5)
So now we have, on the bottom:
(2n^2)(n-5)(n+5)
All together, we have:
(n-5)(n+4)(n)(n+5)
-------------------
(2n^2)(n-5)(n+5)
The (n+5)s and the (n-5)s cancel each other out. So we're left with:
(n+4)(n)
--------
2n^2
That's:
n^2 + 4n
--------
2n^2
Can factor n out :
n(n+4)
-----
n(2n)
You're left with:
(n+4) / (2n)
I put a lot in here. So feel free to ask specific questions. Maybe someone else on the board can explain without as much detail.
Wow let me just say EXTRA THANK YOU. the way how you detailed it, it is very good yes its a lot but well understandable i can see what you mean what to do. Gee this is a better explanation than my own instructor or even the book......thank you....
I'm glad I could help. To be honest, I don't figure out a lot of these math problems before I post them. I just start typing and explain what I'm doing as I go along. I have, in the past, had to erase entire posts and start over when I realized I made a mistake in the 2nd step. LOL
Glad this answer helped.
Matt
Hello! It seems like you are looking for an explanation on how to multiply fractions. Multiplying fractions involves multiplying the numerators (top numbers) together and multiplying the denominators (bottom numbers) together.
Let's look at the example you provided:
(n^2-n-20)/(2n^2) times (n^2+5n)/(n^2-25)
To start, we can factorize the expressions to simplify them:
(n^2-n-20) can be factored as (n-5)(n+4)
Thus, we have:
((n-5)(n+4)(n^2+5n)) / ((2n^2)(n^2-25))
Next, we can simplify further by factoring (n^2+5n):
(n^2+5n) can be factored as n(n+5)
Now, our expression becomes:
((n-5)(n+4)(n)(n+5)) / ((2n^2)(n-5)(n+5))
Next, we notice that (n+5) and (n-5) appear in both the numerator and denominator. These terms cancel each other out, leaving us with:
(n+4)(n) / (2n^2)
We can further simplify by factoring "n" out from the numerator and denominator:
n(n+4) / n(2n)
Now, the "n" terms cancel out, and we are left with:
(n+4) / (2n)
So, the multiplication of the given fractions simplifies to (n+4) / (2n).
I hope this explanation helps! Let me know if you have any further questions.