Canceling an increment reveals a limiting pattern without defining the original quotient at zero.
Expanding the numerator gives h(2a+h). For h≠0, cancellation is valid. The right-hand side approaches 2a as h approaches zero from either side. This is the derivative of x² at a, even though the original quotient is undefined at h=0.
An expression equal for h≠0 need not share the original domain at h=0.