Square Root Problem: Solving for m in s=k√(1+m)/(1-m) | Help & Tips

[triden]

Homework Statement

$$s=k\sqrt{\frac{1+m}{1-m}}$$ , solve for m

Homework Equations

The Attempt at a Solution

Honestly I am stumped, but I do know there is a trick to it. I can't quite remember, but it might have something to do with taking the reciperical or the inverse...maybe the conjugate? Just need a little help getting started.

Thanks,
Chris

 

[Mark44]

Something that would be helpful is to divide both sides by k.
The equation then becomes
$$\frac{s}{k} = \sqrt{\frac{1 + m}{1 - m}}$$
Now, what operation gets rid of square roots?

 

[triden]

Ok, got rid of the root by squaring. Now I have this. How can I isolate the m variable?

$$\frac{s^{2}}{k^{2}} = \frac{1+m}{1-m}$$

 

[Mark44]

Multiply both sides by k², then multiply both sides by (1 - m). If you expand both sides, you should be able to rearrange things to get the terms with m on one side, and all the others on the other side.

 

[Mark44]

Something you said at the beginning deserves a comment:

Honestly I am stumped, but I do know there is a trick to it.

There are probably a few occasions where solving an equation requires some trick that you have to know, but most of the time it's done by plain old mathematical understanding.