## How to calculate $\lim_{x\to 0} (\frac{(5x + 1)^{20} – (20x + 1)^{5}}{\sqrt[5]{1 + 20x^{2}}-1})$ without the rule of L’Hôpital?

$$\lim_{x\to 0} (\frac{(5x + 1)^{20} – (20x + 1)^{5}}{\sqrt[5]{1 + 20x^{2}}-1})$$

Hello! I need to solve this limit. I had solved it with the rule of L’Hôpital, but i can’t without it. I tried multiplicatio using Special Limits, but i simplified it only to $$\lim_{x\to 0} (\frac{e^{100x} – e^{100x}}{e^{4x^2}-1})$$ Please help me, I must solve it using only Special Limits and simple transformations. I can’t use derivatives.