User:Virusys/Temp/Q1


 * $$x[n] = -\frac{1}{3}\left(\frac{1}{2}\right)^n u[n] - \frac{4}{3}(2)^n u[-n -1] $$


 * $$X(z) = \sum_{n=-\infty}^{\infty} -\frac{1}{3}\left(\frac{1}{2}\right)^n u[n] - \frac{4}{3}(2)^n u[-n -1] z^{-n} $$
 * $$X(z) = \left [ \sum_{n=0}^{\infty} -\frac{1}{3}\left(\frac{1}{2}\right)^n - \sum_{n=-\infty}^{-1}-\frac{4}{3}(2)^n \right ] z^{-n} $$
 * $$X(z) = \sum_{n=0}^{\infty} -\frac{1}{3}\left(\frac{1}{2}\right)^n z^{-n} - \sum_{n=-\infty}^{-1}-\frac{4}{3}(2)^n z^{-n} $$
 * $$X(z) = \sum_{n=0}^{\infty} -\frac{1}{3}\left(\frac{1}{2}z^{-1}\right)^n - \sum_{n=-\infty}^{-1}-\frac{4}{3}(2z^{-1})^n $$
 * $$X(z) = -\frac{1}{3}\left(\frac{1}{1 - \frac{1}{2}z^{-1}}\right) - \frac{4}{3}\left(1 - \left(\frac{1}{1-2z^{-1}}\right)\right)$$
 * $$X(z) = -\frac{1}{3}\left(\frac{z}{z - \frac{1}{2}}\right) - \frac{4}{3}\left(1 - \left(\frac{z}{z-2}\right)\right) $$
 * $$X(z) = -\frac{1}{3}\left(\frac{2z}{2z - 1}\right) - \frac{4}{3}\left(\frac{-2}{z-2}\right) $$
 * $$X(z) = -\frac{2z}{6z - 3} + \frac{8}{3z-6} $$
 * $$X(z) = \frac{-6z^2 + 60z - 24}{18z^2 - 45z + 18} $$
 * $$X(z) = \frac{-2z^2 + 20z - 8}{6z^2 - 15z + 6} $$
 * $$X(z) = \frac{-2(z^2 + 10z + 4)}{3(2z-1)(z-2)} $$