If \( a: b=c: d \), and \( e: f=g: h \), prove that \[ a e+b f: a e-b f=c g+d h: c g-d h \]

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If \( a: b=c: d \), and \( e: f=g: h \), prove that
\[
a e+b f: a e-b f=c g+d h: c g-d h
\]
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