remember [tex]\frac{\frac{a}{b}}{\frac{c}{d}}=(\frac{a}{b})(\frac{d}{c})=\frac{ad}{bc}[/tex]
try to combine fractions in numerator and denomenator
numerator: [tex]\frac{1}{x}+\frac{2}{y}[/tex]
make common denom
multiply left one by [tex]\frac{y}{y}[/tex] and right one by [tex]\frac{x^2}{x^2}[/tex]
[tex]\frac{y}{yx^2}+\frac{2x^2}{yx^2}=\frac{2x^2+y}{yx^2}[/tex]
denomenator
[tex]\frac{5}{x}-\frac{6}{y^2}[/tex]
make common denom
multiply left one by [tex]\frac{y^2}{y^2}[/tex] and right one by [tex]\frac{x}{x}[/tex]
[tex]\frac{5y^2}{xy^2}-\frac{6x}{xy^2}=\frac{5y^2-6x}{xy^2}[/tex]
combining we get
[tex]\frac{\frac{1}{x^2}+\frac{2}{y}}{\frac{5}{x}-\frac{6}{y^2}}=[/tex]
[tex]\frac{\frac{2x^2+y}{yx^2}}{\frac{-6x+5y^2}{xy^2}}=[/tex]
[tex](\frac{2x^2+y}{yx^2})(\frac{xy^2}{-6x+5y^2})=[/tex]
[tex]\frac{2x^3y^2+xy^3}{-6x^3y+5x^2y^3}=[/tex]
[tex](\frac{2x^2y+y^2}{-6x^2+5xy})(\frac{xy}{xy})=[/tex]
[tex](\frac{2x^2y+y^2}{-6x^2+5xy})(1)=[/tex]
[tex]\frac{2x^2y+y^2}{-6x^2+5xy}[/tex]
