Question

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

Answer 1

We have the rational expression $\frac{2x^{5}-6x^{2}+4x4y}{2x}$; 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:
$\frac{2x(x^{5}-6x+2(2y)}{2x}$
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 $x^{5}-6x+4y$.