Simplifying a Rational Function with Intermediate Variables

[Cosine12]

Homework Statement

Hi, i have been trying to solve this equation for the past 2 hours but am not getting anywhere near the given answer. If anyone can solve this it would be greatly appreciated! Thank you.

Homework Equations

The answer is circled in red and was derived from the line above it. (picture attached)

The Attempt at a Solution

 

[Dr. Courtney]

Looks like a simple matter to apply FOIL and simplity, with due care in execution.

 

[Cosine12]

Thats what i did but unfortunately i keep getting different values.

 

[donpacino]

show us the steps you take

 

[Cosine12]

I thought i could start with the easy part the denominator but then i don't know what to do with the Z's and end up as shown in picture, aaa my head hurts lol.

 

[donpacino]

I thought i could start with the easy part the denominator but then i don't know what to do with the Z's and end up as shown in picture, aaa my head hurts lol.

just treat the z's like you would any other variable

 

[Cosine12]

Am not getting anywhere with this tbh.. i think il leave this for now as i wasted too much time on it. Thanks for the help anyway.

 

[donpacino]

Am not getting anywhere with this tbh.. i think il leave this for now as i wasted too much time on it. Thanks for the help anyway.

as was previously stated use foil...
you should brush up on your algebra

 

[William White]

My advice would be to sign up for a Wolfram Alpha account.

Its a great resource for helping with such problems.

Enter your equation, and you will get a step-by-step solution.

From there, you will be able to see how to do the algebra.

 

[SammyS]

Homework Statement

Hi, i have been trying to solve this equation for the past 2 hours but am not getting anywhere near the given answer. If anyone can solve this it would be greatly appreciated! Thank you.

Homework Equations

The answer is circled in red and was derived from the line above it. (picture attached)

The Attempt at a Solution

Actually, you're not solving an equation. This is just simplifying the given form for the function.

I suggest that you define some intermediate variables in order to simplify the look of this expression:

Let: $\ a=e^{-0.1}z^{-1}\$, $\ b=e^{-0.2}z^{-1}\$, $\ c=z^{-1}\$.
Multiply the numerator & denominator by 2.​

You get: $\displaystyle \ \frac{(1-a)(1-b)-2(1-a)(1-c)-(1-c)(1-a)}{2(1-a)(1-b)} \ .$

Simplify that, then do the reverse substitution.