Find the limit: $\lim\limits_{x\to1}\dfrac{x^{1/5}-1}{x^{1/3}-1}$ Find the limit of $$\lim_{x\to 1}\frac{x^{1/5}-1}{x^{1/3}-1}$$
How should I approach it?  I tried to use L'Hopital's Rule but it's just keep giving me 0/0.

Hint Take $x=t^{15}$. Then use long division, or $$\frac{t^a-1}{t-1}=1+t+t^2+\cdots+t^{a-1}$$
You can also think about derivatives of $x^{1/3},x^{1/5}$ at $x=1$.
