I really deriving the equation for this?

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To derive the formula, start by rearranging the equations to isolate all A terms on one side and all B terms on the other. Next, apply the kinetic energy balance equation and the momentum balance equation. Divide the resulting equations to simplify the relationship between the variables. This method will lead to the boxed equations as required by the professor. Following these steps will clarify the derivation process.
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Homework Statement


My professor wants to see how to derive the formula. Basically get from the first two lines in the bracket to the two lines that are boxed.

Homework Equations


I have attached the picture of the relevant equations
 

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Start out by getting all the A terms in each of the equations on one side of the equation, and all the B terms on the other side of the equation. Then, divide the resulting kinetic energy balance equation by the resulting momentum balance equation.
 
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