simplify f(x)=(x^2-x)/(x-1)

Question

If f(x)=(x^2-x)/(x-1) and g(x)=x

is it true that f=g?

Answer 1

While (x^2-x)/(x-1) does simplify to x, it is not true that g(x) and f(g) are not equivalent. Because f(x)=x except at x=1 and is undefined at x=1. Meanwhile g(1)=1.