Solving a Fraction: Calculate Velocity of an Orbit

[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?

 

[trollcast]

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.

 

[HallsofIvy]

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