fraction(N1, D1) - fraction(N2, D2) = {?}
N1 / D1 - N2 / D2
\qquad = \blue{\dfrac{N1 \times F1}{D1 \times F1}} -
\green{\dfrac{N2 \times F2}{D2 \times F2}}
\qquad = \blue{\dfrac{N1 * F1}{LCM}} -
\green{\dfrac{N2 * F2}{LCM}}
\qquad = \dfrac{\blue{N1 * F1} -
\green{N2 * F2}}{LCM}
\qquad = fraction(F1 * N1 - F2 * N2, LCM)
\qquad = fractionReduce(F1 * N1 - F2 * N2, LCM)