Rewrite a symbolic expression in terms of a specific subexpression

Question

I need to rewrite a symbolic expression in terms of a specific subexpression.

Consider the following scenario:

• expression f with 2 variables a, b

• subexpression c = a / b

  syms a b c
  f = b / (a + b) % = 1 / (1 + a/b) = 1 / (1 + c) <- what I need
  

Is there a way to achieve this?

Edit:

The step from 1 / (1 + a/b) to 1 / (1 + c) can be achieved by calling

subs(1 / (1 + a/b),a/b,c)

So a better formulated question is:

Is there a way to tell MATLAB to 'simplify' b / (a + b) into 1 / (1 + a/b)?

Just calling simplify(b / (a + b) makes no difference.

Answer 1

Simplification to your desired form is not automatically guaranteed, and in my experience, isn't likely to be achieved directly through simplify-ing as I've noticed simplification rules prefer rational polynomial functions. However, if you know the proper reducing ratio, you can substitute and simplify

>> syms a b c
>> f = b / (a + b);
>> simplify(subs(f,a,c*b))
ans =
1/(c + 1)

>> simplify(subs(f,b,a/c))
ans =
1/(c + 1)

And then re-substitute without simplification, if desired:

>> subs(simplify(subs(f,a,c*b)),c,a/b)
ans =
1/(a/b + 1)

>> subs(simplify(subs(f,b,a/c)),c,a/b)
ans =
1/(a/b + 1)