Final answer:
To find the ratio of x to y, rearrange the equation and simplify.
Step-by-step explanation:
To find the ratio of x to y, we can start by rearranging the equation given:
6/x + 9 = 2/y + 3
Subtract 3 from both sides:
6/x + 6 = 2/y
Now, we can cross multiply:
6y = 2x(x + 6)
Expand the brackets:
6y = 2x^2 + 12x
Next, we can divide both sides of the equation by 2:
3y = x^2 + 6x
Finally, we can simplify the equation to:
x^2 + 6x - 3y = 0
This is the ratio of x to y in terms of an equation.