1.7: Past-paper question 2

Given that

is the binomial expansion, in ascending powers of $\displaystyle x$, of $\displaystyle (1 + Ax)^n$

where $\displaystyle A$ and $\displaystyle n$ are rational numbers,

(a) find the value of $\displaystyle A$ and the value of $\displaystyle n$

(b) Hence find the value of the coefficient of $\displaystyle x^3$

Give your answer in the form $\displaystyle \frac{p}{q}$ where $\displaystyle p$ is a prime number and $\displaystyle q$ is an integer.