Originally Posted by

**Foxlion** $\displaystyle F(x)=\frac{x^4-5x^3+\sqrt{x}}{x^2} $

solution attempt: Book asks one to to try solving two ways once with quotient rule and once simplifying first. I have shown here only the quotient rule solution as that is giving me enough trouble to warrant a post

With quotient rule,

$\displaystyle [(4x^3-15x^2+\frac{1}{2}x^\expfrac{-1/2})(x^2)] - [(2x)(x^4-5x^2+\sqrt{x})] $

$\displaystyle = [4x^5-5x^4+\frac{1}{2} x^\expfrac{3/2}] - [2x^5-10x^4+2x(x)^\expfrac{1/2}]$

$\displaystyle = \frac{2x^5+5x^4+\frac{1}{2}x^\expfrac{3/2}-2x(x)^\expfrac{1/2}}{x^4}$

this is where I am reluctant to continue as I'm unsure how to go about simplifying the exponents, in doing so I end up with:

$\displaystyle \frac{2x+5+\frac{1}{2}x-2x}{x^6} $