# Reciprocals of Reciprocals

Number Theory Level 4

$\large{\begin{cases} \frac{1}{a} - \frac{1}{b} - \frac{1}{c} + \frac{1}{d} &=& \frac{1}{20} \\ a - b - c + d &=& 0 \\ \end{cases} }$

Let $$a < b < c < d$$ be positive integers satisfying the system of equations above. If $$\gcd ( a, b, c , d ) = 1$$, then what is the value of $$\dfrac{c}{a} - \dfrac{b}{d}$$?

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