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This is electronics related but more algebra than electronics. I'm a bit rusty having not done anything involving mathemtics for night-on 10 years.

I have the following thing to solve for $R_X$:

$V_o=V_i(\frac{R_T}{R_X + R_T})$

I have got to:

$\frac{V_o}{V_i} = \frac{R_T}{R_X+R_T}$

But I'm stuck there.

Now I know the answer to this is as follows (from wikipedia):

$R_X=\frac{R_T}{\frac{V_i}{V_o} - 1}$

Unfortunately I do not know the workings and rules to get from the former to the latter. Can anyone explain the steps or point me in the right direction?

(this is for voltage dividers if anyone is interested).

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up vote 4 down vote accepted


$$\frac{V_o}{V_i} = \frac{R_T}{R_X+R_T}$$

reciprocate both sides

$$\frac{V_i}{V_o} = 1+ \frac{R_X}{R_T}$$

and you should be able to proceed...

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Excellent - thank you so much. That's really helped me a lot. Best Regards! – cjs Apr 7 '11 at 10:36

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