Question

Simplify.

2x5 - 6x2 + 4x4y
-------------------------
2x

Answer 1

We have the rational expression
`(2x^(5)-6x^(2)+4x4y)/(2x)`; to simplify it, we are going to try to find a common factor in the numerator, and, if we are luckily, that common factor will get rid of the denominator
`2x`.
Notice that in the denominator all the numbers are divisible by two, so 2 is part of our common factor; also, all the terms have the variable
`x`, and the least exponent of that variable is 1, so
`x` will be the other part of our common factor. Lets put the two parts of our common factor together to get
`2x`.
Now that we have our common factor, we can rewrite our numerator as follows:

`(2x(x^(5)-6x+2(2y))/(2x)`
We are luckily, we have
`2x` in both numerator and denominator, so we can cancel those out:

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

`x^5-6x+4y`

We can conclude that the simplified version of our rational function is
`x^(5)-6x+4y`.