How can I reduce this expression to e^{mx}?

[Saladsamurai]

Homework Statement

I at a point in a derivation where I have the expression:

$$A = \frac{e^{mx} - e^{2ml - mx}}{1-e^{2ml}}$$

I have double checked my work leading up to this point, so i am confident my expression for 'A' is correct. I am supposed to reduce it to

$$A = e^{mx}$$

but I am not seeing the trick here. I have tried numerous approaches from factoring the denominator and various arrangements of the numerator. I have a feeling it is one of those random tricks i need. Any thoughts?

 

[Mark44]

Homework Statement

I at a point in a derivation where I have the expression:

$$A = \frac{e^{mx} - e^{2ml - mx}}{1-e^{2ml}}$$

I think you might have a sign error in the exponent on the first term in the numerator.

Assuming this is the case for the moment, you have
$$A = \frac{e^{-mx} - e^{2ml - mx}}{1-e^{2ml}}$$
$$= \frac{e^{-mx} - e^{2ml}\cdot e^{ -mx}}{1-e^{2ml}}$$
$$= \frac{e^{-mx}(1 - e^{2ml})}{1-e^{2ml}} = e^{-mx}$$

I have double checked my work leading up to this point, so i am confident my expression for 'A' is correct. I am supposed to reduce it to

$$A = e^{-mx}$$

but I am not seeing the trick here. I have tried numerous approaches from factoring the denominator and various arrangements of the numerator. I have a feeling it is one of those random tricks i need. Any thoughts?

 

[Saladsamurai]

Homework Statement

I at a point in a derivation where I have the expression:

$$A = \frac{e^{mx} - e^{2ml - mx}}{1-e^{2ml}}$$

I have double checked my work leading up to this point, so i am confident my expression for 'A' is correct. I am supposed to reduce it to

$$A = e^{-mx}$$

but I am not seeing the trick here. I have tried numerous approaches from factoring the denominator and various arrangements of the numerator. I have a feeling it is one of those random tricks i need. Any thoughts?

I'm sorry it's supposed to come out to be a positive exponent. That is,

$$A = e^{mx}$$

I have edited OP.

 

[Mark44]

In that case, I think your error is in the second term in the numerator.
$$A = \frac{e^{mx} - e^{2ml + mx}}{1-e^{2ml}}$$

$$= \frac{e^{mx} - e^{2ml}\cdot e^{ mx}}{1-e^{2ml}}$$

$$= \frac{e^{mx}(1 - e^{2ml})}{1-e^{2ml}} = e^{mx}$$