FactoringDenominator is an option for
Collect2. It is taken into account only when the option
Numerator is set to True. If
FactoringDenominator is set to any function f,
this function will be applied to the denominator of the fraction. The
default value is False, i.e. the denominator will be left
unchanged.
ex = (x1 a^2 + y 1 a^2 + 2 a b + x2 b^2 + y2 b^2)/(a + b + c^2 +
2 c d + d^2)\frac{a^2 \;\text{x1}+a^2 y+2 a b+b^2 \;\text{x2}+b^2 \;\text{y2}}{a+b+c^2+2 c d+d^2}
Collect2[ex, a, b]\frac{a^2 (\text{x1}+y)}{a+b+c^2+2 c d+d^2}+\frac{b^2 (\text{x2}+\text{y2})}{a+b+c^2+2 c d+d^2}+\frac{2 a b}{a+b+c^2+2 c d+d^2}
Collect2[ex, a, b, Numerator -> True]\frac{a^2 (\text{x1}+y)+2 a b+b^2 (\text{x2}+\text{y2})}{a+b+c^2+2 c d+d^2}
Collect2[ex, a, b, Numerator -> True, FactoringDenominator -> Simplify]\frac{a^2 (\text{x1}+y)+2 a b+b^2 (\text{x2}+\text{y2})}{a+b+(c+d)^2}