Simplify this equation: (x+y)/(y^2-xy-y+x) + (y+1)/(xy-x-y+1) + (x+1)/(x^

Date: 8/18/95
From: Anonymous

Message from Talk_Daemon@forum ... 
talk: connection requested by outside user

Dr.M: Hi.

Q: are you dr.math?

Dr.M: Yes, that's one of the things I do. There are other Dr. Maths too.

Q: I have a problem with an exercise in my homework could you help me? 

Dr.M: Well, sure. Normally, you'd send us an e-mail message, but I'll help
      you out if I can.

Q: ok thank you       well this is the problem I'll take time to write it 
   (x+y)/(y^2-xy-y+x)+(y+1)/(xy-x-y+1)+(x+1)/(x^2-xy-x+y) 
   I need to 

Dr.M: Simplify?

Q: yes

Dr.M: Okay. Well, The first thing you should probably do is try to factor the
      denominators of each of the fractions.  Have you tried to do that?

Q: yes but i can

Dr.M: Did you have any luck?

Q: I can't sorry

Dr.M: That's okay. No problem. Well, things are harder to factor when they 
      have two variables than when they have only one. 

Q: yes of course

Dr.M: In the first fraction, you've got a y^2. So if it factors, both of the terms 
      are probably going to have a y in them, right? So they'll look like 
      y + something and y + something else. 

Q: ok

Dr.M: So that's one thing. Also, you're going to have to have an x in there 
      somewhere, and a negative sign. So try making one of the somethings 
      a negative x. So one factor is y-x, and the other is y + something.

Q: ok

Dr.M: With that, it's at least something to go on. 

Q: ok i understand.

Dr.M: Can you do the factoring now? (Note that the last fraction is just like the 
      first one, with x and y reversed) 

Q: yes Can i contact you later to verify

Dr.M: Sure, that's fine.

Q: ok thank you

Dr.M: No problem.

Q: good bye i'll close connection

Dr.M: See ya!

[Connection closing. Exiting]

Date: 8/18/95
From: Anonymous

Message from Talk_Daemon@forum at 14:25 ... 
talk: connection requested by outside user

Q: it's me again

Dr.M: Did you have any luck with the factoring? 

Q: yes i found this      (x+y)/(y-1)(y-x)

Dr.M: first one's good...

Q: (x+y)/(y-1)(y-x)+(y+1)/(x-1)(y-1)

Dr.M: second one's good...

Q: (x+y)/(y-1)(y-x)+(y+1)/(x-1)(y-1)-(x+1)/(y-x)(y-x) 

Dr.M: I'm not sure about that last one, though. Wasn't the denominator 
      (x^2 - xy - x + y)?

Q: yes

Dr.M: Well, if you multiply out (y-x)(y-x) you don't get that. 

Q: I found my error

Dr.M: Good.

Q: is it (y-x)(x-1)

Dr.M: Right! (as long as you didn't lose a negative somewhere; I have (x-y)(x-1)). 
      But that's essentially right. 

Q: Can I simplify more?

Dr.M: Yes, now what you can do is combine the three fractions.  Remember that 
      when you add fractions, you have to find a common denominator. 

Q: ok

Dr.M: So you figure out what the common denominator is by finding all the 
      different factors of the three denominators (keeping in mind that x-y and y-x 
      are just negatives).

Q: Is the common denominator (y-1)(y-x)(x-1)? 

Dr.M: Yes! good stuff. So now you need to make each fraction have that 
      denominator. To do that, you figure out what each fraction is missing, and 
      then you multiply its top and bottom by that missing piece. 

Q: ok could you wait for me?

Dr.M: Sure.

Q: ok just a second.      Here we go         (x+y)(x-1)+

Dr.M: first one's good...

Q: (x+y)(x-1)+(y+1)(y-x)-

Dr.M: second one's good...

Q: (x+y)(x-1)+(y+1)(y-x)-(x+1)(y-1)/common denominator 

Dr.M: Right!  So now all you have to do is multiply out the top stuff, and
      combine like terms and simplify.

Q: one second...       x^2-x+yx-y+y^2-yx+y-x-xy+x-y+1

Dr.M: That's what I got. So now you just combine and cancel.

Q: ok         x^2+y^2-x-y-xy+1

Dr.M: Yup, that's what I got.

Q: Can I simplify more??

Dr.M: I don't think so. I think that's it!

Q: It was easy with your help

Dr.M: Hey, no problem. Most of them don't get too much harder than that. 
      You'll probably be able to do them better now that you have done that one.

Q: Can i contact you on other ocassion?

Dr.M: Sure, although the best way is to write an e-mail to us.  We try to answer 
      them within 24 hours.

Q: ok

Dr.M: Do you know the addresss?

Q: is it dr.math@mathforum.org?

Dr.M: Yes, that's it. We'll look forward to hearing from you.

Q: thank you and sorry for my english

Dr.M: No problem! Your English is great.

Q: Is that right??

Dr.M: It's not your first language?

Q: Yeah.

Dr.M: Well, I'll hear from you.

Q: good bye, i'll close connection