I find the method that I'm being taught to change a fraction with a binomial denominator into a mixed expression quite confusing and am wondering if there is an alternative method?

For example:

The method I'm being shown is to place the fraction in the form of long division. I'm not sure how to write that out using Latex.

Is this the only way to approach these problems? I find it quite confusing and quite frankly a little "messy" to work in that fashion.