- #1

AxiomOfChoice

- 533

- 1

[tex]

e^{1/z} + \frac{1}{1-e^{1/z}} = w.

[/tex]

How in the world should I go about doing that?

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- Thread starter AxiomOfChoice
- Start date

- #1

AxiomOfChoice

- 533

- 1

[tex]

e^{1/z} + \frac{1}{1-e^{1/z}} = w.

[/tex]

How in the world should I go about doing that?

- #2

HallsofIvy

Science Advisor

Homework Helper

- 43,021

- 970

[tex]u+ \frac{1}{1- u}= w[/tex]

Multiply both sides by 1- u to get u(1- u)+ 1= w(1- u) or [itex]u- u^2+ 1= w- uw[/itex] which equivalent to the quadratic equation [itex]u^2- (1+w)u+ w-1= 0[/itex]. Use the quadratic formula to solve that, then solve [itex]e^{1/z}= u[/math] by taking the logarithm of both sides.

- #3

AxiomOfChoice

- 533

- 1

[tex]u+ \frac{1}{1- u}= w[/tex]

Multiply both sides by 1- u to get u(1- u)+ 1= w(1- u) or [itex]u- u^2+ 1= w- uw[/itex] which equivalent to the quadratic equation [itex]u^2- (1+w)u+ w-1= 0[/itex]. Use the quadratic formula to solve that, then solve [itex]e^{1/z}= u[/math] by taking the logarithm of both sides.

Great. Thanks. This was my original approach, but for some reason I wasn't sure if I could make that change of variables and apply the quadratic formula like you did. But you've confirmed my intuition, so I'm going with it!

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