X(z)= (1+3z-1+11/6 z-2+1/3 z-3)/(1+5/6 z-1+1/6 z-2 )?
A. 1+2z -1+(1/6 z-1)/(1+5/6 z-1+1/6 z-2 )
B. 1-2z -1+(1/6 z-1)/(1+5/6 z-1+1/6 z-2 )
C. 1+2z -1+(1/3 z-1)/(1+5/6 z-1+1/6 z-2)
D. 1+2z -1-(1/6 z-1)/(1+5/6 z-1+1/6 z-2 )
Answer:A
X(z)= (1+3z-1+11/6 z-2+1/3 z-3)/(1+5/6 z-1+1/6 z-2 )?
A. 1+2z -1+(1/6 z-1)/(1+5/6 z-1+1/6 z-2 ) B. 1-2z -1+(1/6 z-1)/(1+5/6 z-1+1/6 z-2 ) C. 1+2z -1+(1/3 z-1)/(1+5/6 z-1+1/6 z-2) D. 1+2z -1-(1/6 z-1)/(1+5/6 z-1+1/6 z-2 )
Explanation: First, we note that we should reduce the numerator so that the terms z-2 and z -3 are eliminated. Thus we should carry out the long division with these two polynomials written in the reverse order. We stop the division when the order of the remainder becomes z -1. Then we obtain