A LTI system has transfer function $H(z)=\frac{1-\frac{1}{5}{z}^{-1}}{1-\frac{7}{12}{z}^{-1}+\frac{1}{12}{z}^{-2}},|z|>\frac{1}{3}.$ The input to the system is $x[n]=2(\frac{1}{5}{)}^{n}u[n].$ What is output $y[n]?$

$y[n]=8(\frac{1}{3}{)}^{n}u[n]-6(\frac{1}{4}{)}^{n}u[n]$

$y[n]=6(\frac{1}{3}{)}^{n}u[n]-8(\frac{1}{4}{)}^{n}u[n]$

$y[n]=-8(\frac{1}{3}{)}^{n}u[n]+6(\frac{1}{4}{)}^{n}u[n]$

$y[n]=-6(\frac{1}{3}{)}^{n}u[n]+8(\frac{1}{4}{)}^{n}u[n]$