Answer
$\dfrac{\dfrac{1}{y^{2}}+\dfrac{2}{3}}{\dfrac{1}{y}-\dfrac{5}{6}}=\dfrac{2(2y^{2}+3)}{y(6-5y)}$
Work Step by Step
$\dfrac{\dfrac{1}{y^{2}}+\dfrac{2}{3}}{\dfrac{1}{y}-\dfrac{5}{6}}$
Evaluate the sum indicated in the numerator and the substraction indicated in the denominator:
$\dfrac{\dfrac{1}{y^{2}}+\dfrac{2}{3}}{\dfrac{1}{y}-\dfrac{5}{6}}=\dfrac{\dfrac{3+2y^{2}}{3y^{2}}}{\dfrac{6-5y}{6y}}=...$
Evaluate the division and simplify if possible:
$...=\dfrac{3+2y^{2}}{3y^{2}}\div\dfrac{6-5y}{6y}=\dfrac{(3+2y^{2})(6y)}{(6-5y)(3y^{2})}=\dfrac{(2y^{2}+3)(2)}{(6-5y)(y)}=...$
$...=\dfrac{2(2y^{2}+3)}{y(6-5y)}$
