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.

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