Handling a Fraction

I'm trying to figure out how to calculate the velocity of an orbit at apogee or perigee and I've figured out the derivation of the equation except for this one fraction... I replaced the radius quantities for x and y for ease of viewing.

$\frac{x-y}{x^2 - y^2} = \frac{1}{x + y}$

Can anybody break this down for me barney-style?

Recognitions:
Gold Member
 Quote by James Brady I'm trying to figure out how to calculate the velocity of an orbit at apogee or perigee and I've figured out the derivation of the equation except for this one fraction... I replaced the radius quantities for x and y for ease of viewing. $\frac{x-y}{x^2 - y^2} = \frac{1}{x + y}$ Can anybody break this down for me barney-style?
Express the $$x^2-y^2$$ as the difference of 2 squares.

Then it will cancel to give the right hand fraction.
 Recognitions: Gold Member Science Advisor Staff Emeritus As long as x- y is not equal to 0, $(x^2- y^2)/(x- y)= (x- y)(x+ y)/(x- y)= x+ y$.