Handling a Fraction

1. Feb 13, 2013

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?

2. Feb 13, 2013

trollcast

Express the $$x^2-y^2$$ as the difference of 2 squares.

Then it will cancel to give the right hand fraction.

3. Feb 13, 2013

HallsofIvy

Staff Emeritus
As long as x- y is not equal to 0, $(x^2- y^2)/(x- y)= (x- y)(x+ y)/(x- y)= x+ y$.