NEG1S \dfrac{N1}{D1} \div NEG2S \dfrac{N2}{D2} = {?}
Dividing by a fraction is the same as multiplying by the reciprocal of the fraction.
The reciprocal of NEG2S \dfrac{N2}{D2} is
NEG2S \dfrac{D2}{N2}.
Therefore:
NEG1S \dfrac{N1}{D1} \div NEG2S \dfrac{N2}{D2} =
NEG1S \dfrac{N1}{D1} \times NEG2S \dfrac{D2}{N2}
\phantom{NEG1S \dfrac{N1}{D1} \times NEG2S \dfrac{D2}{N2}} =
\dfrac{NEG1SN1 \times NEG2SD2}{D1 \times N2}
\phantom{NEG1S \dfrac{N1}{D1} \times NEG2S \dfrac{D2}{N2}} =
\dfrac{NUMERATOR}{DENOMINATOR}
The numerator and denominator have a common divisor of GCD, so we can simplify:
\dfrac{NUMERATOR}{DENOMINATOR} =
\dfrac{NUMERATOR \div GCD}{DENOMINATOR \div GCD} =
fractionReduce(NUMERATOR, DENOMINATOR)