[tex]\bf \begin{cases}
f(x)=2x-1\\
g(x)=x^2+3x-1
\end{cases}
\\\\[-0.35em]
\rule{34em}{0.25pt}\\\\
f(x)+g(x)\implies (2x-1)+(x^2+3x-1)\implies 2x+3x-1-1+x^2
\\\\\\
x^2+5x-2
\\\\[-0.35em]
~\dotfill[/tex]
[tex]\bf f(x)-g(x)\implies (2x-1)-(x^2+3x-1)\implies 2x-1-x^2-3x+1
\\\\\\
-x^2-x
\\\\[-0.35em]
~\dotfill\\\\
f(x)\cdot g(x)\implies (2x-1)\cdot (x^2+3x-1)
\\\\\\
\stackrel{2x(x^2+3x-1)}{2x^3+6x^2-2x}~~+~~\stackrel{-1(x^2+3x-1)}{(-x^2-3x+1)}\implies 2x^3+5x^2-5x+1
\\\\[-0.35em]
~\dotfill\\\\
\cfrac{f(x)}{g(x)}\implies \cfrac{2x-1}{x^2+3x-1}[/tex]
the division doesn't simplify any further.
