Answer:
[tex] \dfrac{-y(2x^2 + y)}{x(6x - 5y^2)} [/tex]
Step-by-step explanation:
[tex] \dfrac{\frac{1}{x^2}+\frac{2}{y}}{\frac{5}{x}-\frac{6}{y^2}} = [/tex]
To eliminate the denominators of the main numerator and denominator, we multiply the numerator and denominator of the main fraction by the LCD of all small denominators.
The LCD of x^2, y, x, and y^2 is x^2y^2.
[tex] = \dfrac{x^2y^2 \times (\frac{1}{x^2}+\frac{2}{y})}{x^2y^2 \times (\frac{5}{x}-\frac{6}{y^2})} [/tex]
[tex] = \dfrac{y^2 + 2x^2y}{5xy^2 - 6x^2} [/tex]
[tex] = \dfrac{y(y + 2x^2)}{x(5y^2 - 6x)} [/tex]
[tex] = \dfrac{-y(2x^2 + y)}{x(6x - 5y^2)} [/tex]
