\begin{aligned}\dfrac{x^{3}}{x^{n+3}}=\dfrac{x^{3}}{x^{n}\cdot x^{3}}=\dfrac{1}{x^{n}}\\ \rightarrow x^{n}\left( \dfrac{1}{x^{n}\cdot 3}-\dfrac{1}{x^{n}}\right) \end{aligned}
\begin{aligned}\dfrac{\left( \dfrac{x^{n}}{x^{n-3}}-\dfrac{x^{n}}{x^{n}}\right) }{\left( x-1\right) }\\ =\dfrac{x^{3}-1}{\left( x-1\right) }=\dfrac{\left( x-1\right) \left( x^{2}+x+1\right) }{\left( x-1\right) }\\ =\left( x^{2}+x+1\right) \end{aligned}