a-b/b-a

opivfx · #1 $Old$ November 5th, 2009, 09:01 AM

Hello everybody!
There is a problem on my pre-calculus study guide that I don't understand.
It's been about 2 years since I took any formal math class(pre-calculus honors in high school).

Quote:

The problem: Find the difference and simplify.
5
----
y-5
-
y
----
y-5

So you get,

Quote:

5-y
----
y-5

Now here's the part I don't quite understand.
On the answer sheet, the answer is -1.

The only way I can see how this is gotten, is that any a-b/b-a is equal to -1.
I can't seem to find any other examples of this in any of my textbooks though. Am I missing something?

Thank you guys.

Defunkt · #2 $Old$ November 5th, 2009, 09:35 AM

Note that $\frac{a-b}{b-a} = \frac{(-1)(-1)(a-b)}{b-a} = \frac{(-1)(b-a)}{b-a} = -\frac{b-a}{b-a} = -1$