simplify-z-2-1-z-1-1-z-2-1-1-z-1-z-

Question Number 172515 by Mikenice last updated on 28/Jun/22

s i m p l i f y

\frac{z^{2} - 1}{z - 1} \div \frac{1}{z^{2} + 1} \times \frac{1}{z + \frac{1}{z}}

Answered by Rasheed.Sindhi last updated on 28/Jun/22

\frac{z^{2} - 1}{z - 1} \div \frac{1}{z^{2} + 1} \times \frac{1}{z + \frac{1}{z}}

= \frac{(z - 1) (z + 1)}{z - 1} \times \frac{z^{2} + 1}{1} \times \frac{1}{\frac{z^{2} + 1}{z}}

= \frac{(z + 1)}{1} \times \frac{z^{2} + 1}{1} \times \frac{z}{z^{2} + 1}

= z (z + 1)