## Algebra: A Combined Approach (4th Edition)

$\dfrac{\dfrac{1}{y^{2}}+\dfrac{2}{3}}{\dfrac{1}{y}-\dfrac{5}{6}}=\dfrac{2(2y^{2}+3)}{y(6-5y)}$
$\dfrac{\dfrac{1}{y^{2}}+\dfrac{2}{3}}{\dfrac{1}{y}-\dfrac{5}{6}}$ 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: $...=\dfrac{3+2y^{2}}{3y^{2}}\div\dfrac{6-5y}{6y}=\dfrac{(3+2y^{2})(6y)}{(6-5y)(3y^{2})}=\dfrac{(2y^{2}+3)(2)}{(6-5y)(y)}=...$ $...=\dfrac{2(2y^{2}+3)}{y(6-5y)}$