\displaystyle NEG1S \frac{N1}{D1} \div NEG2S \frac{N2}{D2} = {?}
Turn into a multiplication problem:
\displaystyle {} = NEG1S \frac{N1}{D1} \times NEG2S \frac{D2}{N2}
Reduce terms with common factors:
\displaystyle {} = NEG1S \frac{SIMP_N1}{SIMP_D1} \times NEG2S \frac{SIMP_D2}{SIMP_N2}
Combine into one fraction:
\displaystyle {} = \frac{NEG1 * SIMP_N1 \times NEG2 * SIMP_D2}{SIMP_D1 \times SIMP_N2}
Simplify:
\displaystyle {} = fractionReduce(NEG1 * N1 * NEG2 * D2, D1 * N2)