Quotient rule application

Identify $f(x) = x^3 + 2x - 1$ and $h(x) = 4x+5$ (using $h$ to avoid clashing with $g$'s name). Then $f'(x) = 3x^2 + 2$ and $h'(x) = 4$. The quotient rule states $g'(x) = \dfrac{f'(x)h(x) - f(x)h'(x)}{[h(x)]^2}$.

Substituting gives $g'(x) = \dfrac{(3x^2+2)(4x+5) - (x^3+2x-1)(4)}{(4x+5)^2}$. Expanding the numerator: $(3x^2+2)(4x+5) = 12x^3 + 15x^2 + 8x + 10$, and $4(x^3+2x-1) = 4x^3+8x-4$. Subtracting gives $12x^3+15x^2+8x+10 - 4x^3-8x+4 = 8x^3 + 15x^2 + 14$. So $g'(x) = \dfrac{8x^3+15x^2+14}{(4x+5)^2}$.