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

$$\lim_{y\to32}\frac{\sqrt[5]{y^2} - 3\sqrt[5]{y} + 2}{y - 4\sqrt[5]{y^3}}$$
taking $\sqrt[5]{y}=x$
we have that
$$\lim_{x\to2}\frac{x^2-3x+2}{x^5-4x^3}=\lim_{x\to2}\frac{x^2-x-2x+2}{x^3(x^2-4)}=$$
$$=\lim_{x\to2}\frac{x(x-1)-2(x-1)}{x^3(x-2)(x+2)}=\lim_{x\to2}\frac{(x-1)(x-2)}{x^3(x-2)(x+2)}$$
$$=\lim_{x\to2}\frac{(x-1)}{x^3(x+2)}=1/32$$
