Simplifying a Rational Function with Intermediate Variables

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Discussion Overview

The discussion revolves around simplifying a rational function involving intermediate variables. Participants are attempting to solve a specific equation presented in a homework context, with a focus on algebraic manipulation and simplification techniques.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant expresses frustration in solving the equation and requests assistance, noting a discrepancy between their results and the expected answer.
  • Another participant suggests using the FOIL method for simplification, emphasizing careful execution.
  • A different participant reports that they also obtained different values despite applying the suggested method.
  • There is a request for the steps taken in the attempted solution to better understand the issue.
  • One participant mentions difficulty with the variables involved, particularly with the Z's, and expresses confusion about how to proceed.
  • Another participant reiterates the advice to treat the Z's like any other variable.
  • Frustration is expressed by a participant who feels they have spent too much time on the problem without progress.
  • A suggestion is made to use Wolfram Alpha as a resource for step-by-step solutions to aid in understanding the algebra involved.
  • One participant clarifies that the task is about simplifying the expression rather than solving an equation, and proposes defining intermediate variables to aid in simplification.
  • The same participant provides a specific approach involving the definition of intermediate variables and a suggested simplification process.

Areas of Agreement / Disagreement

Participants generally express frustration and confusion regarding the simplification process, with no clear consensus on the correct approach or solution. Multiple viewpoints on methods and techniques remain present throughout the discussion.

Contextual Notes

Some participants may be missing foundational algebraic skills, as indicated by the suggestions to brush up on algebra. There are also indications of unresolved steps in the simplification process, particularly concerning the treatment of variables.

Cosine12
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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

 

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Looks like a simple matter to apply FOIL and simplity, with due care in execution.
 
Thats what i did but unfortunately i keep getting different values.
 
show us the steps you take
 
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.
 

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Cosine12 said:
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
 
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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.
 
Cosine12 said:
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
 
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.
 
  • #10
Cosine12 said:

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

screen-shot-2015-07-10-at-14-40-54-png.85751.png

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.
 

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