Question

Simplify the expression, show your work

Answer 1

Answer:

$\dfrac{-y(2x^2 + y)}{x(6x - 5y^2)}$

Step-by-step explanation:

$\dfrac{\frac{1}{x^2}+\frac{2}{y}}{\frac{5}{x}-\frac{6}{y^2}} =$

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.

$= \dfrac{x^2y^2 \times (\frac{1}{x^2}+\frac{2}{y})}{x^2y^2 \times (\frac{5}{x}-\frac{6}{y^2})}$

$= \dfrac{y^2 + 2x^2y}{5xy^2 - 6x^2}$

$= \dfrac{y(y + 2x^2)}{x(5y^2 - 6x)}$

$= \dfrac{-y(2x^2 + y)}{x(6x - 5y^2)}$