Question

Given f(x) = 2x - 1 and g(x) = x^2 + 3x - 1, find f(x) + g(x), f(x) - g(x), f(x) • g(x), and (f/g)(x)

Answer 1

$\bf \begin{cases} f(x)=2x-1\\ g(x)=x^2+3x-1 \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ f(x)+g(x)\implies (2x-1)+(x^2+3x-1)\implies 2x+3x-1-1+x^2 \\\\\\ x^2+5x-2 \\\\[-0.35em] ~\dotfill$

$\bf f(x)-g(x)\implies (2x-1)-(x^2+3x-1)\implies 2x-1-x^2-3x+1 \\\\\\ -x^2-x \\\\[-0.35em] ~\dotfill\\\\ f(x)\cdot g(x)\implies (2x-1)\cdot (x^2+3x-1) \\\\\\ \stackrel{2x(x^2+3x-1)}{2x^3+6x^2-2x}~~+~~\stackrel{-1(x^2+3x-1)}{(-x^2-3x+1)}\implies 2x^3+5x^2-5x+1 \\\\[-0.35em] ~\dotfill\\\\ \cfrac{f(x)}{g(x)}\implies \cfrac{2x-1}{x^2+3x-1}$

the division doesn't simplify any further.