Given that $\displaystyle A*B = C*D$, prove that $\displaystyle \frac{D – B}{\frac{B + D}{2}} = \frac{C – A}{\frac{A + C}{2}}$.

Attempted solution:

$\displaystyle A*B = C*D$

$\displaystyle \Rightarrow \frac{B}{D} = \frac{C}{A}$

$\displaystyle \Rightarrow 1 - \frac{B}{D} = 1 - \frac{C}{A}$

$\displaystyle \Rightarrow \frac{D}{D} - \frac{B}{D} = \frac{A}{A} - \frac{C}{A}$

$\displaystyle \Rightarrow \frac{D - B}{D} = \frac{A - C}{A}$ ....

Where do I go from here?