Dividing Rational Expressions!

Please help with this prob. It is over fifty and I cant finish it all by my self in just 8 hours time so can anybody help me with this 15 items of expressions?

here are they:


2a+2b__________ a^2-b^2
------ Divided by ---------
a^2__________ 4a

____________________________

a^2-4__________ a^2-a-2
------ Divided by ----------
a^2-1__________ a^2+a-2


____________________________

4a^2-25 ________ 12a+30
-------- Divided by---------
a^2-16 ________ 2a^2+8a


____________________________

a^4-b^4________ a^2+b^2
-------- Divided by---------
5a-5b___________ 5


___________________________

a^2-b^2
--------- Divided by a+b
a^2+b^2

x^2-13x+42_________ 2x^2-13x-7
----------- Divided by------------
6+x-x^2____________ 2x^2-5x-3


______________________________________

x^2+2x^2________ 1-4x^2
----------Divided by----------
9-x^2____________3x+2x^2


______________________________________

a^3-ab^3_________a^2+ab
----------Divided by------------
a^2b_____________3ab+3b^2


______________________________________

a^4-b^4_________2a^2+2b^2
---------Divided by------------
3a+3n_______________6


______________________________________

m^2-3m+2___________2-m
-----------Divided by--------
m^2-1______________1-m


______________________________________


2a^2-11a+12_________a^3+4a^2
-------------Divided by------------
27-18a_______________6a^3-96a


______________________________________

1___________ 1___________1
---Dividedby-----Divided by-----
xy_________xy^2________x^2y


______________________________________

_2x-7_____________7-2x
( ----)^2 Dividedby (----)^4
__9________________3


______________________________________

6x^2_________21________x^2
-----dividedby----dividedby----
6x-14_______9x-21_______35


______________________________________

x^2____________x+y__________x
--------dividedby-----dividedby(----)^2
x^2-y^2________x-y__________x+y


______________________________________



Thanks for the ones who can help ;-)

Sincerely,

Hardheaded


*note: this (^) symbolizes that the number at the right of it is raised
______and n symbolizes that all nos. inside the pharenthese is raised
(-----)^2
m



one again,


THANKS!

Quote:

---

Originally Posted by Hardheaded

Please help with this prob. It is over fifty and I cant finish it all by my self in just 8 hours time so can anybody help me with this 15 items of expressions?

here are they:


2a+2b__________ a^2-b^2
------ Divided by ---------
a^2__________ 4a

____________________________

a^2-4__________ a^2-a-2
------ Divided by ----------
a^2-1__________ a^2+a-2


____________________________

4a^2-25 ________ 12a+30
-------- Divided by---------
a^2-16 ________ 2a^2+8a


____________________________

a^4-b^4________ a^2+b^2
-------- Divided by---------
5a-5b___________ 5


___________________________

a^2-b^2
--------- Divided by a+b
a^2+b^2

---

I will do just first problem because I really can't write without LaTex, someone else on forum will help you with others:

1)
[(2a+2b)/a^2] / [(a^2-b^2)/4a] = [2(a+b)/a^2] * [4a/[(a+b)(a-b)]] =
8/(a^2-ab)

Can anybody answer the remaining items?




Please I desperately need it!

Quote:

---

Originally Posted by Hardheaded

a^2-4__________ a^2-a-2
------ Divided by ----------
a^2-1__________ a^2+a-2

---

I think, rather than try to have someone do all these for you, it would be better to have someone explain what needs to be done.

So, the first thing you need to do with problems like these is factor whatever you can in the numerators and denominators. Then you cancel what you can.

The hardest part of this problem is the factoring, so let's look at the kinds of factoring problems you have here.

First:
a^2 - 4
This is of the form of the difference between two squares:
a^2 - b^2 = (a+b)(a-b)
So
a^2 - 4 = (a+2)(a-2)

a^2 - 1 is similar: a^2 - 1 = (a+1)(a-1)

Now we are left with a^2 - a - 2 and a^2 + a - 2. Typically you can guess at these:
a^2 - a - 2 = (a + _)(a + _)
The missing numbers must be factors of -2 of which there are only 4. So there are only a small number of possibilities here:
(a + 2)(a - 1) = a^2 + a - 2
(a + 1)(a - 2) = a^2 - a - 2
(The other combinations just repeat these factors in a different order.)

As it happens, in the process we also managed to factor a^2 + a - 2.

So the problem, after all the factoring has been done, becomes:
(a+2)(a-2)(a+1)(a-2)
(a+1)(a-1)(a+2)(a-1)

Cancelling the common factors we get:

(a-2)^2
(a-1)^2

All of these problems are done in exactly the same way. Since the only problem I can imagine you would have with these would be factoring, what I would suggest is that you go through these and factor what you can factor. Then make a list of what you are having problems factoring and post those. That would make it much more simple for all of us to help you where you most need it.

-Dan