I'm having difficulties solving this numerical analysis problem: Given the equation $f(x)=0$ and its associated iteration defined by $$x_{n+1}=x_{n}-\frac{[f(x_n)]^2}{f(x_n+f(x_n))-f(x_n)},$$ explain the relationship between this iteration and the Newton-Raphson method. Also, show that $\{x_n\}$ converges to the exact solution of $f(x)=0$ if $x_0$ is close enough to it.
I know the N-R method and its iteration formula, but I don't know how to approach this. Please help.