If \( a: b=c: d \) prove that \[ \left(\frac{1}{a}-\frac{1}{c}\right)-\left(\frac{1}{b}-\frac{1}...
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0If \( a: b=c: d \) prove that
\[
\left(\frac{1}{a}-\frac{1}{c}\right)-\left(\frac{1}{b}-\frac{1}{d}\right)=\frac{(a-b)(a-c)}{a b c} \text {. }
\]
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