How can we show the equivalence of two optimizations?

Question

How can we show the equivalence of (a) and (b)?

$\max(x^TAx)$ subject to $\|x\|=1$....(a)

$\max{\frac{x^TAx}{x^Tx}}$...(b)

Answer 1

$$\max \frac{x^TAx}{x^Tx} = \max \frac{x^TAx}{\|x\|^2} = \max \frac{x^T}{\|x\|} A \frac{x}{\|x\|}$$

Rewrite $u = x/\|x\|$ where $u$ always has norm $1$. So the two are equivalent.