This will be a little rough without LaTeX...

(c - d)/(1/d - 1/c)

We wish to remove the fractions in the denominator. So we want to subtract:

1/d - 1/c = c/(cd) - d/(cd) = (c - d)/cd

So:

(c - d)/(1/d - 1/c) = (c - d)/[(c - d)/cd]

Now we want to multiply the denominator by cd to remove the fraction. But what we do to the denominator we must do to the numerator:

(c - d)/(1/d - 1/c) = (c - d)/[(c - d)/cd] = [(c - d)(cd)]/(c - d) = cd

It's always good to do to an example.

c = 4, d = 2

(4 - 2)/(1/2 - 1/4) = 2/(1/4) = 8 = 2*4 (Check!)

-Dan