Rat'l Expression: (x^2-y^2-4x+4y)/(x^2-y^2+4x-4y)

[Hayleyanne]

I posted a rational expression problem earlier today and someone posted back (thank you!) but I still don't really understand why thats the answer. Could anyone explain it to me?
this is the problem:

x^2 - y^2 - 4x + 4y
________over_______

x^2 - y^2 + 4x - 4y

 

[Mrspi]

Re: Could someone explain this?

I posted a rational expression problem earlier today and someone posted back (thank you!) but I still don't really understand why thats the answer. Could anyone explain it to me?
this is the problem:

x^2 - y^2 - 4x + 4y
________over_______

x^2 - y^2 + 4x - 4y

Is this what you mean?

x[sup:11s4nvjr]2[/sup:11s4nvjr] - y[sup:11s4nvjr]2[/sup:11s4nvjr] - 4x + 4y
-------------------------------------
x[sup:11s4nvjr]2[/sup:11s4nvjr] - y[sup:11s4nvjr]2[/sup:11s4nvjr] + 4x - 4y

If so, I'd try to factor the numerator, and factor the denominator, and see if the fraction can be reduced.

Let's look at the numerator first:

x[sup:11s4nvjr]2[/sup:11s4nvjr] - y[sup:11s4nvjr]2[/sup:11s4nvjr] - 4x + 4y

Let's group the first two terms together, and the last two terms together:

(x[sup:11s4nvjr]2[/sup:11s4nvjr] - y[sup:11s4nvjr]2[/sup:11s4nvjr]) - 4x + 4y

Factor the first two terms as a difference of two squares, and remove a common factor of -4 out of the last two terms:

[(x + y)(x - y)] - 4(x - y)

Now, there is a common factor of (x - y) in both terms...remove that common factor, and you have

(x - y) (x + y - 4)

Do the same sort of process on the denominator...

After you've done that, see if the resulting fraction can be reduced.

If you're still having trouble, please repost showing us what you've done.

 

[stapel]

I posted a rational expression problem earlier today and someone posted back (thank you!) but I still don't really understand why thats the answer.

In future, kindly post replies and follow-ups to threads within the original thread, rather than starting new threads (new conversations) on the old topic.

Note: The answer was what it was because of the factoring that the tutor displayed. To learn how to factor, please study some online lessons. (You will need many more tools and techniques than were displayed in just this one thread.)

Thank you.

Eliz.