We have the rational expression [tex] \frac{2x^{5}-6x^{2}+4x4y}{2x} [/tex]; 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 [tex]2x[/tex]. 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 [tex]x[/tex], and the least exponent of that variable is 1, so [tex]x[/tex] will be the other part of our common factor. Lets put the two parts of our common factor together to get [tex]2x[/tex]. Now that we have our common factor, we can rewrite our numerator as follows: [tex] \frac{2x(x^{5}-6x+2(2y)}{2x} [/tex] We are luckily, we have [tex]2x[/tex] in both numerator and denominator, so we can cancel those out: [tex]x^{5}-6x+2(2y)[/tex] [tex]x^5-6x+4y[/tex]
We can conclude that the simplified version of our rational function is [tex]x^{5}-6x+4y[/tex].