Maxima: How to factor a expression in an expected form

Question

I have an expression:

(b+2*ab+a+1)/c

I want to use Maxima to factor the equation treating (b+1) as a factor.

i.e. I want the expression in the following form:

[(b+1)(1+a)+ab]/c

Any help would be appreciated.

Answer 1

Well, my advice is first isolate the numerator, then get the quotient and remainder after dividing by b + 1, then put the pieces back together.

(%i1) display2d : false $
(%i2) expr : (b + 2*a*b + a + 1)/c $
(%i3) num (expr);
(%o3) 2*a*b+b+a+1
(%i4) divide (num (expr), b + 1);
(%o4) [2*a+1,-a]
(%i5) first(%o4) * (b + 1) + second(%o4);
(%o5) (2*a+1)*(b+1)-a
(%i6) (first(%o4) * (b + 1) + second(%o4)) / denom (expr);
(%o6) ((2*a+1)*(b+1)-a)/c
(%i7) is (equal (%o6, expr));
(%o7) true

Note that divide returns two values; first is the quotient and second is the remainder.