Solving for X in a Fractional Equation

  • Context: High School 
  • Thread starter Thread starter rede96
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Discussion Overview

The discussion revolves around solving for x in the fractional equation X ÷ (X + Y) = Z, with participants exploring various steps and methods for transposing the formula. The conversation includes attempts to solve the equation with specific values for y and z, as well as requests for clarification on the algebraic process involved.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant asks how to solve for x given y and z in the equation X ÷ (X + Y) = Z.
  • Another participant suggests multiplying both sides by (X + Y) to begin the solution process.
  • A participant expresses difficulty in remembering the steps and requests a demonstration using specific values for y and z.
  • There is a suggestion to subtract ZX from both sides of the equation, leading to the expression X - ZX = ZY.
  • Participants discuss the need to factor x from the left side of the equation and express uncertainty about the subsequent steps.
  • One participant mentions discovering a potential solution through trial and error, stating X = (Y / (1-Z)) - Y.
  • Another participant recommends using an online tool, Wolfram Alpha, to check the answer and view the steps involved in solving the equation.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the solution process, as there are multiple suggestions and expressions of uncertainty regarding the algebraic steps involved. The discussion remains unresolved with various approaches being proposed.

Contextual Notes

Participants express limitations in recalling algebraic techniques and the steps required to isolate x, indicating a reliance on memory and prior knowledge that may not be fully intact.

rede96
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Hi,

I should know this but havn't done any transposition of formula for a long, long while :)

If I know y and z, how can I solve for x in the following formula:

X ÷ (X + Y) = Z

Thanks.
 
Last edited:
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hi rede96! :smile:

multiply both sides by (x+y) :wink:
 
tiny-tim said:
hi rede96! :smile:

multiply both sides by (x+y) :wink:

Thanks tiny-tim.

So I would get X = Z (X + Y) or X = ZX + ZY

But as I am feeling very mathematically challenged today, :smile: can you demonstrate solving for x when y = 28 and z = 0.3 please.
 
Step 2: Subtract ZX from both sides of the equation.
 
HallsofIvy said:
Step 2: Subtract ZX from both sides of the equation.

Ok, so now I have X - ZX = ZY.

I assume that there are a few more steps but I'll be dammed if I can remember. :blushing:

From memory I know I need to remove the Z from the ZX on left hand side of the equation, but can't figure out how.

Rather than go through this one step at a time, I would very much appreciate it if someone could give me the answer then I can work backwards.

Just by playing with the numbers I figured out that X = (Y / (1-Z)) - Y but have not figured out yet how to get there!
 
Last edited:
Step 3: Factor x from the two terms on the left side.
I'm hopeful you can figure out step 4 (the last step) on your own.

rede96 said:
I assume that there are a few more steps but I'll be dammed if I can remember.
Does that mean you are a river? :biggrin:
 
Mark44 said:
Step 3: Factor x from the two terms on the left side.
I'm hopeful you can figure out step 4 (the last step) on your own.

Does that mean you are a river? :biggrin:


Well if you mean do I feel that I am about to burst then yes! :biggrin: So either dammed or damned would do!

Thanks for the help, still not figured it but am really busy at the mo, so will have a look later.

Red.
 
When you are done, you can use http://www.wolframalpha.com" to check your answer. You can type in things like "x/(x+y)=z, solve for x". It will also show you the steps in doing so if you choose "show steps".
 
Last edited by a moderator:
KingNothing said:
When you are done, you can use http://www.wolframalpha.com" to check your answer. You can type in things like "x/(x+y)=z, solve for x". It will also show you the steps in doing so if you choose "show steps".

Cool, thanks. :biggrin: Just wish I could remember all this stuff!
 
Last edited by a moderator:
  • #10
rede96 said:
Ok, so now I have X - ZX = ZY.

Hint: X = 1X (one times X), so this becomes

1X - ZX = ZY

What can you do with the left-hand side now, so you end up with a single X?
 

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