How do you simplify #\frac { z } { ( z - 1) ^ { 2} } - \frac { 1} { ( z - 1) ( z + 3) }#?

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Answer 1 · 2017-04-14T10:47:40

#(z+1)^2/((z-1)^2(z+3))#

#z/(z-1)^2-1/((z-1)(z+3))#

To get a common denminatro, we multiply the numerator and the denominator of the first term by #(z+3)# and those of the second term y #(z-1)#,

#=(z(z+3))/((z-1)^2(z+3))-(z-1)/((z-1)^2(z+3))#

By combining them together,

#=(z^2+3z-(z-1))/((z-1)^2(z+3))#

By simplifying the numerator,

#=(z^2+2z+1)/((z-1)^2(z+3))#

#=(z+1)^2/((z-1)^2(z+3))#

I hope that this was clear.