[tex]\frac{f(x)}{g(x)} =?[/tex]
Since you know f(x) = 2x and g(x) = 3x^3, you can substitute that into the function
[tex]\frac{f(x)}{g(x)} =?[/tex]
[tex]\frac{2x}{3x^3} =?[/tex]
When a variable(x or y) with an exponent is divided by another variable with an exponent, you subtract the exponents, only if the variables are the same.
For example:
[tex]\frac{x}{y}[/tex] Since the variables on the top and bottom are not the same, you can't simplify it (or its already simplified)
[tex]\frac{x^3}{x^2} =x^{3-2} =x^1[/tex]
[tex]\frac{y^5}{y^7}=y^{5-7}=y^{-2} = \frac{1}{y^2}[/tex] (when an exponent is negative, you move it to the other side of the fraction to make the exponent positive)
[tex]\frac{2x}{3x^3} =?[/tex]
[tex]\frac{2x}{3x^3}= (\frac{2}{3})x^{1-3}= (\frac{2}{3})x^{-2} = (\frac{2}{3})\frac{1}{x^2}[/tex] Since you can't simplify 2/3, you get:
(not sure if this is how it should look ---> (2/3)x^(1-3) but i'm assuming it is)
[tex]\frac{2}{3x^2}[/tex]
