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- Homework Statement
- If ##\frac {z-1} {z+1} = ni## and ## Z\ne -1##, then can we simply criss-cross the denominators of the two sides so that LHS is multiplied by 1 and RHS is multiplied by ##z+1##? This is part of a bigger problem, but I just wanted to clear my doubts on whether this approach is possible.

- Relevant Equations
- None

I am not sure why criss-cross approach would work here, but it seems to get the answer. What would be the reason why we could use this approach?

$$\frac {z-1} {z+1} = ni$$

$$\implies \frac {z-1} {z+1} = \frac {ni} {1}$$

$$\implies {(z-1)} \times 1= {ni} \times {(z+1)}$$

$$\frac {z-1} {z+1} = ni$$

$$\implies \frac {z-1} {z+1} = \frac {ni} {1}$$

$$\implies {(z-1)} \times 1= {ni} \times {(z+1)}$$

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