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The $z$-Transform of a sequence $x[n]$ is given as $X(z)=2z+4-4/z+3/z^{2}$. If $y[n]$ is the first difference of $x[n]$, then $Y(z)$ is given by

  1. $2z+2-8/z+7/z^{2}-3/z^{3}$
  2. $-2z+2-6/z+1/z^{2}-3/z^{3}$
  3. $-2z-2+8/z-7/z^{2}+3/z^{3}$
  4. $4z-2-8/z-1/z^{2}+3/z^{3}$
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