Question

Simplify the expression, show your work

Answer 1

`(-y(2x^2 + y))/(x(6x - 5y^2))`

Explanation:

`((1)/(x^2)+(2)/(y))/((5)/(x)-(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.

`= (x^2y^2 * ((1)/(x^2)+(2)/(y)))/(x^2y^2 * ((5)/(x)-(6)/(y^2)))`

`= (y^2 + 2x^2y)/(5xy^2 - 6x^2)`

`= (y(y + 2x^2))/(x(5y^2 - 6x))`

`= (-y(2x^2 + y))/(x(6x - 5y^2))`