calculus - I need compute a rational limit that involves roots

I need compute the result of this limit without l'hopital's rule, I tried different techniques but I did not get the limit, which is 1/32, I would appreciate if somebody help me. Thanks.

$$\lim_{y\to32}\frac{\sqrt[5]{y^2} - 3\sqrt[5]{y} + 2}{y - 4\sqrt[5]{y^3}}$$

Answer

$$\lim_{y\to32}\frac{\sqrt[5]{y^2} - 3\sqrt[5]{y} + 2}{y - 4\sqrt[5]{y^3}}$$

We set $y^{\frac{1}{5}}=x$

When $y \to 32, x \to 2$

So,we have:

$$\lim_{x \to 2} \frac{x^2-3x+2}{x^5-4x^3}=\lim_{x \to 2} \frac{(x-1) (x-2)}{x^3(x^2-4)}=\lim_{x \to 2} \frac{(x-1)(x-2)}{x^3(x-2)(x+2)}=\lim_{x \to 2} \frac{x-1}{x^3(x+2)}=\frac{1}{8 \cdot 4}=\frac{1}{32}$$