# Control engineering problem

1. Jul 10, 2015

### Cosine12

1. The problem statement, all variables and given/known data
Hi, i have been trying to solve this equation for the past 2 hours but am not getting anywhere near the given answer. If any one can solve this it would be greatly appreciated!! Thank you.

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

3. The attempt at a solution

#### Attached Files:

• ###### Screen Shot 2015-07-10 at 14.40.54.png
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2. Jul 10, 2015

### Dr. Courtney

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

3. Jul 10, 2015

### Cosine12

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

4. Jul 10, 2015

### donpacino

show us the steps you take

5. Jul 10, 2015

### 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.

#### Attached Files:

• ###### Screen Shot 2015-07-10 at 17.58.06.png
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6. Jul 10, 2015

### donpacino

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

7. Jul 10, 2015

### 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.

8. Jul 10, 2015

### donpacino

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

9. Jul 11, 2015

### William White

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.

10. Jul 11, 2015

### SammyS

Staff Emeritus

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.