Question

EPCAR-2012! ME AJUDEM POR FAVOR!

Answer 1

$\mathrm{(a+b)^2=a^2+2ab+b^2}\\ \mathrm{(a^3-b^3)=(a-b)(a^2+ab+b^2)}\\ \mathrm{(a+b)(a-b)=a^2-b^2}\\\\ \mathrm{y=\dfrac{\dfrac{(a^2+2ab+b^2)(a^3-b^3)}{(a^2-b^2)(a^2+ab+b^2)}}{\bigg(\dfrac{a^2-ab}{2a}\bigg)}=\dfrac{\dfrac{(a+b)^2(a^3-b^3)}{(a+b)(a-b)(a^2+ab+b^2)}}{\bigg(\dfrac{a-b}{2}\bigg)}=}\\\\\\ \mathrm{=\dfrac{(a+b)(a^3-b^3)}{(a^3-b^3)}\times\dfrac{2}{(a-b)}=2\bigg(\dfrac{a+b}{a-b}\bigg)=2\bigg(\dfrac{x}{x^{-1}}\bigg)=2x^2}\\\\\\ \mathbf{y=2x^2}$