Originally Posted by

**topsquark** Perhaps this is a bit sloppy (but then I tend to make problems a bit rougher than they need to be.) Start with the two equaitons:

$\displaystyle \frac{1}{x} + \frac{1}{y} = 1$

and

$\displaystyle x + y = a$

Then we know that

$\displaystyle \frac{x + y}{xy} = 1$

Put the second equation in:

$\displaystyle \frac{a}{x(a - x)} = 1$

or

$\displaystyle x^2 - ax + a = 0$

Now start from x + y = a and y = mx.

$\displaystyle x + mx = a$

giving

$\displaystyle x = \frac{a}{m + 1}$

Put this into the $\displaystyle x^2 - ax + a = 0$ equation to cancel the x and you are done.

-Dan