function that corresponds to Newton's method

Question is if $\displaystyle f(x) = x^4 + x - 19$ then which of the following functions correspond to Newton's method $\displaystyle x_{n + 1} = g(x_n)$

Answer is given as $\displaystyle

g(x) = \frac{{3x^4 + 19}}{{4x^3 + 1}}

$

But I would have thought it would be

$\displaystyle

g(x) = \frac{{ - x^4 + 4x^3 - x + 20}}{{4x^3 + 1}}

$

considering

$\displaystyle

\begin{array}{l}

x_{n + 1} = x_n - \frac{{f(x)}}{{f'(x)}} \\

x_{n + 1} = x_n - \frac{{x^4 + x - 19}}{{4x^3 + 1}} \\

x_{n + 1} = \frac{{4x^3 + 1}}{{4x^3 + 1}} - \frac{{x^4 + x - 19}}{{4x^3 + 1}} \\

x_{n + 1} = \frac{{ - x^4 + 4x^3 - x + 20}}{{4x^3 + 1}} \\

\end{array}

$

Could someone clarify what I am doing wrong or not interpreting correctly. Thanks