# Why This Equation Equals -1

1. Feb 18, 2008

### mike_302

This is not a very difficult question, by any means, and I see that the answer does equal -1, but I do not see the mathematical steps that go on to prove that (y-2)/(2-y)=-1 .. Can someone show me the steps that go through that? Thanks in advance.

2. Feb 18, 2008

### ivanetski

Dude...

1) (y-2)/(2-y)=-1
2) (y-2)=-1(-y+2)
3) (y-2)=(y-2)

Wait a bit and I'll post the same in TeX.

3. Feb 18, 2008

### ivanetski

Better way.

$$\frac{y-2}{2-y}=\frac{(y-2)(y+2)}{(2-y)(2+y)}=\frac{y^2-4}{4-y^2}=-1$$

4. Feb 18, 2008

### mike_302

lol, ok sorry. That was posted slightly incorrectly the first time. Basically, the textbook says "simplify: (y-2)/(2-y) " and the back of the book gives the final answer to be -1, so I can't do the left side right side stuff

5. Feb 18, 2008

### mike_302

ahh, yes, I see your second post now . That does seem to be better. Thanks

6. Feb 18, 2008

### mike_302

so basically what I do in your second post is I multiply the bottom and top by the conjugate of the denominator?

7. Feb 18, 2008

### ivanetski

In the future, could you please post your homework/assignment questions in the homework forum?

This forum is more about theoretical discussions.

8. Feb 18, 2008

### ivanetski

Wow, I'm stupid...

$$\frac{y-2}{2-y}=\frac{-1(2-y)}{2-y} =-1$$

This is what you get for not doing any maths for almost a year.

9. Feb 18, 2008

### mike_302

OH! Jeeeze. I see, lol, Thanks. and, yes. Normally I post in the math homework forums but I think I just clicked on the wrong link and got here. I didn't notice that, sorry.

10. Feb 18, 2008

### JasonRox

I thought it was about general math.

11. Feb 18, 2008

### Hurkyl

Staff Emeritus
(y-2)/(2-y) = -1 is an equation

(y-2)/(2-y) is not an equation; it's an expression.

12. Feb 18, 2008

### Tom Mattson

Staff Emeritus
It's -1 for all real numbers y not equal to 2.