Associated Topics || Dr. Math Home || Search Dr. Math

### 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
```
Associated Topics:
High School Equations, Graphs, Translations

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search