I'm trying to get the denominators to equal each other. The denominators are 4x^3 and 2x. What do I multiply 2x with to get 4x^3?

Expert Answers
lemjay eNotes educator| Certified Educator

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`

atyourservice | Student

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`