Projective and flat modules over polynomial rings

Question

Let $R = \mathbb{C}[x]$ be a ring of polynomials in $x$ with coefficients in the field of complex numbers. I have the following two questions:

1. How can I show that a projective $R$-module $A$ is flat.

2. Let $N = R[t]/ (xt-1)$. If we view $N$ as an $R$-module, is $N$ flat? Here $R[t]$ is a polynomial in variables $t$ and $x$.

Honestly I have no idea where to start but I know my definitions.

Answer 1

From the comments:

1. Free modules are flat and direct summands of flat modules are flat.
2. You should notice that $N$ is a localization of $R$ and thus flat.