Answer
$\dfrac{5y^2-1}{y+2}$
Work Step by Step
$\dfrac{5-\dfrac{1}{y^2}}{\dfrac{1}{y}+\dfrac{2}{y^2}} = \dfrac{\dfrac{5y^2-1}{y^2}}{\dfrac{y^2+2y}{y^3}} = \dfrac{\dfrac{5y^2-1}{y^2}}{\dfrac{y(y+2)}{y^3}} = \dfrac{\dfrac{5y^2-1}{y^2}}{\dfrac{y+2}{y^2}} = \dfrac{y^2(5y^2-1)}{y^2(y+2)} = \dfrac{5y^2-1}{y+2}$
