Need Help With Simplifying

[ItalianFX]

My roommate is doing some math and he can't figure this one out. I tried helping him, but I can't figure it out either.

Simplify, if you can.


http://img457.imageshack.us/img457/4367/simplifydj8.png

[Magic_Man]

Y / (1/X - 1/Y)

Y / (Y/(XY) - X/(XY))

Y / ( (Y-X)/(XY) )

Y*XY / (Y-X)

= X*Y^2 / (Y-X)


~MagicMan

[ItalianFX]

How did you go from

Y / (1/X - 1/Y)

to

Y / (Y/(XY) - X/(XY))

[Magic_Man]

[ QUOTE ]
How did you go from

Y / (1/X - 1/Y)

to

Y / (Y/(XY) - X/(XY))

[/ QUOTE ]

Look at just the denominator:
1/X - 1/Y

I'm going to multiply each term by 1, but in a clever way:

1/X * (Y/Y) - 1/Y * (X/X)

= Y/YX - X/YX

= (Y-X)/(YX)

The basic idea is that you want the denominators to be the same, so you "crossmultiply." One denominator is X, one denominator is Y, so you can make the common denominator XY.

Does that make sense?

~MagicMan

[ItalianFX]

Yes, that is what I thought you did, but wanted to check.

Thanks!