Determining decreasing sequence For a sequence $x_{n+1}=4x_n-x_{n-1}$, $x_1=4, x_2=15$, show that the sequence $\frac{x_{n+1}}{x_n}$ is decreasing
I know from calculating that $\frac{x_{n+1}}{x_n}-\frac{x_{n}}{x_{n-1}}=\frac{-1}{x_nx_{n-1}}$, but I can't seem to prove that.
Any tips please?

Sketch:
0. Set $y_n=\frac{x_n}{x_{n-1}}$ for $n>1$.
1. Prove that $x_n>0$, therefore $y_n>0$
2. Determine the sign of first difference $y_3-y_2$ (it is negative for 
the actual parameters ($x_1,x_2=4,15$). 
3. Consider the difference of $y_n$:
$
y_{n+1}-y_{n}=(4-\frac{1}{y_n})-(4-\frac{1}{y_{n-1}})=\frac{y_{n}-y_{n-1}}{y_{n}y_{n-1}}
$

It shows us, that the sign of the difference does not change ($y_n>0$).
