Simplify an expression with the given substitution of another expression

Suppose an expression expr2=expr3(expr1*expr2)+expr2... How to make a simplification or substitution such that expr1 can be replaced by a single letter A?

from sympy import Function
f= Function('f')
from sympy import *
x,y=symbols('x y',real=True)
A,B,C=symbols("A B C")

a=1/f(x)
b=(1/f(x)).diff(x)
c=(1/f(x)).diff(x,2)

func=1/f(x)*(1-f(x)**2*y)
expr=func.diff(x,2)

where

expr
(-2*y*(f(x)*Derivative(f(x), (x, 2)) + Derivative(f(x), x)**2) + 4*y*Derivative(f(x), x)**2 + (y*f(x)**2 - 1)*(Derivative(f(x), (x, 2)) - 2*Derivative(f(x), x)**2/f(x))/f(x))/f(x)

Clearly, expr contain the expression c

c
(-Derivative(f(x), (x, 2)) + 2*Derivative(f(x), x)**2/f(x))/f(x)**2

However, when I tried

expr.subs(c,C)
expr.expand().subs(c,C)
expr.simplify().subs(c,C)
expr.expand().simplify().subs(c,C)

None of those attempts worked.

How to simplify an expression with the given substitution of another expression?

from sympy import *
init_printing()

f= Function('f')
x,y=symbols('x y',real=True)
A,B,C=symbols("A B C")

a=1/f(x)
b=(1/f(x)).diff(x)
c=(1/f(x)).diff(x,2)

func=1/f(x)*(1-f(x)**2*y)
expr=func.diff(x,2)
expr

Let's look at c:

c

Clearly, expr doesn't contain c, not directly. You can verify it with expr.has(c) which returns False. We can spot the numerator of c (with the sign flipped), but the denominator is applied to different expressions. That's why SymPy doesn't see c into expr: they are structurally different. But we can work on that.

num, den = fraction(c)
num, den

Now, we look for -num and replace it with C * den:

new_expr = expr.subs(-num, C * den)
new_expr

You can go a step further: new_expr is a multiplication between 1/f(x) and an addition. Hence, we can apply the distributive property of multiplication:

new_expr2 = Add(*[1 / f(x) * a for a in new_expr.args[1].args])
new_expr2

Here, you can verify that new_expr2.equals(new_expr).