I would expect subs to replace c with 1, but it doesn't. Why?
sage: S.<a, b, c, d, e, f, g> = QQ[]
sage: R.<x> = S[]
sage: ex = (a*x+b)/(c*x + d) - (e*x+f)/(g*c*x + g*d)
sage: ex
((a*g - e)*x + b*g - f)/(c*g*x + d*g)
sage: ex.subs(c=1)
((a*g - e)*x + b*g - f)/(c*g*x + d*g)
sage: ex.subs({c:1})
((a*g - e)*x + b*g - f)/(c*g*x + d*g)
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