Question 52727
You need to have a common denominator for both fractions; hence, the common denominator of {{{(z-1)(z+1)}}}.  So using this common denominator, we need to determine what each of the fractions is with that common denominator.  The first fraction becomes {{{(4(z+1))/((z-1)(z+1))}}}, which simplifies to {{{(4z+4)/(z-1)(z+1)}}}.  The second fraction becomes {{{(2(z-1))/((z-1)(z+1))}}}, which simplifies to {{{(2z-2)/((z-1)(z+1))}}}.  Now, we have the {{{(4z+4)/((z-1)(z+1)) - (2z-2)/((z-1)(z+1))}}}, which simplifies to {{{(4z+4-2z+2)/((z-1)(z+1))}}}.  Now combining like terms we get {{{(2z+6)/((z-1)(z+1))}}}.