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

$$simplify$$$$\frac{z^2-1}{z-1}\mathbf{÷}\frac{1}{z^2+1}\times \frac{1}{z+\frac{1}{z}}$$

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

$$\frac{z^2-1}{z-1}\mathbf{÷}\frac{1}{z^2+1}\times \frac{1}{z+\frac{1}{z}}$$$$=\frac{\left(\cancel{z-1}\right)(z+1)}{\cancel{z-1}}\times \frac{z^2+1}{1}\times \frac{1}{\frac{z^2+1}{z}}$$$$=\frac{(z+1)}{1}\times \frac{\cancel{z^2+1}}{1}\times \frac{z}{\cancel{z^2+1}}$$$$=z(z+1)$$$$$$

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