For h:= $\mathbb{R} \rightarrow \mathbb{R}, x \rightarrow e^{x}-x^2+1$ I know the formula as $$X\_{n+1}=X\_{n}-\frac{f(X\_{n})}{f'(X\_{n})}$$ so this would give me:
$$ X\_{n+1}=X\_{n}-\frac{e^{x}-x^{2}+1}{e^{x}-2x}$$
However my lecture has in his solution the iteration map is: $$\frac{(xe^{x}-x^{2}+e^{2}-1)}{e^{x}-2x}$$

My question is how does he get this which is different to mine and dosen't look to similar to the Newton Raphson formula?