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You must cancel $h$ because direct substitution of $h=0$ into the difference quotient $\frac{f(x+h)-f(x)}{h}$ results in the indeterminate form $0/0$. Algebraic simplification, such as expansion and cancellation for polynomials or rationalization for radicals, removes the singularity at $h=0$, allowing the limit to be evaluated by direct substitution of the simplified expression.

Conditions: The function $f$ is differentiable at $x$.; The difference quotient initially yields a $0/0$ form when $h=0$.; Algebraic manipulation is valid for nonzero $h$.

You must cancel $h$ because direct substitution of $h=0$ into the difference quotient $\frac{f(x+h)-f(x)}{h}$ results in the indeterminate form $0/0$. Algebraic simplification, such as expansion and cancellation for polynomials or rationalization for radicals, removes the singularity at $h=0$, allowing the limit to be evaluated by direct substitution of the simplified expression.

Conditions: The function $f$ is differentiable at $x$.; The difference quotient initially yields a $0/0$ form when $h=0$.; Algebraic manipulation is valid for nonzero $h$.