The LCD of the denominators `2x` and 4x^3 is 4x^3 .
Then, determine the factor that should be multiplied with 2x to get the LCD.
`2x * (?) = 4x^3`
To do so, perform opposite operation.
So, divide 4x^3 by 2x.
`(4x^3)/(2x) = 2x^2`
Therefore, we should multiply the denominator 2x by 2x^2 to get 4x^3.
`2x * 2x^2 =4x^3`
What do I multiply 2x with to get 4x^3?
I would recommend looking at the problem in a different light, this is a method I use and hopefully it helps you too (^_^):
Try seeing 2x as `2xx x` and `4x^3` as `4 xx x ^3`
See the coefficients are one part and the variables as another
Now ask yourself, what do you multiply 2 by to get 4? 2
What do you multiply x by to get `x^3` ? `x^2`
therefore you multiply `2x *2x^2` to get `4x^3`