Proving the Equation (y-2)/(2-y)=-1 for All Real Numbers y ≠ 2

  • Context: High School 
  • Thread starter Thread starter mike_302
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Discussion Overview

The discussion revolves around proving the equation (y-2)/(2-y) = -1 for all real numbers y ≠ 2. Participants explore the mathematical steps involved in simplifying the expression and verifying the equality.

Discussion Character

  • Homework-related, Mathematical reasoning, Technical explanation

Main Points Raised

  • One participant requests clarification on the mathematical steps to prove the equation equals -1.
  • Another participant provides a step-by-step approach to demonstrate the equality, suggesting that (y-2) = -1(-y+2) leads to (y-2) = (y-2).
  • A different method is proposed involving the multiplication of the numerator and denominator by the conjugate, leading to a transformation of the expression.
  • Several participants express confusion about the nature of the expression versus the equation, with one noting that (y-2)/(2-y) is an expression, not an equation.
  • One participant acknowledges a misunderstanding and realizes the simplification process after reviewing the steps provided by others.
  • Another participant mentions that the textbook states the final answer is -1, but they struggle with the left side-right side comparison.
  • There is a suggestion that homework questions should be posted in a designated forum for better context.

Areas of Agreement / Disagreement

Participants generally agree that the expression simplifies to -1 for all real numbers y not equal to 2, but there is some confusion regarding the nature of the expression and the proper forum for such discussions. Multiple approaches to the simplification are presented without a consensus on the best method.

Contextual Notes

Some participants express uncertainty about the definitions of terms used in the discussion, such as "equation" versus "expression." There is also a mention of a lack of recent mathematical practice affecting understanding.

Who May Find This Useful

This discussion may be useful for students seeking to understand algebraic simplifications and the differences between expressions and equations, particularly in the context of homework help.

mike_302
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This is not a very difficult question, by any means, and I see that the answer does equal -1, but I do not see the mathematical steps that go on to prove that (y-2)/(2-y)=-1 .. Can someone show me the steps that go through that? Thanks in advance.
 
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Dude...

1) (y-2)/(2-y)=-1
2) (y-2)=-1(-y+2)
3) (y-2)=(y-2)

Wait a bit and I'll post the same in TeX.
 
Better way.

[tex]\frac{y-2}{2-y}=\frac{(y-2)(y+2)}{(2-y)(2+y)}=\frac{y^2-4}{4-y^2}=-1[/tex]
 
lol, ok sorry. That was posted slightly incorrectly the first time. Basically, the textbook says "simplify: (y-2)/(2-y) " and the back of the book gives the final answer to be -1, so I can't do the left side right side stuff
 
ahh, yes, I see your second post now . That does seem to be better. Thanks
 
so basically what I do in your second post is I multiply the bottom and top by the conjugate of the denominator?
 
mike_302 said:
so basically what I do in your second post is I multiply the bottom and top by the conjugate of the denominator?
Yes. (I had to look up what's a conjugate to answer your question.:shy:)

In the future, could you please post your homework/assignment questions in the homhttps://www.physicsforums.com/forumdisplay.php?f=152"um?


This forum is more about theoretical discussions.
 
Last edited by a moderator:
Wow, I'm stupid...

[tex]\frac{y-2}{2-y}=\frac{-1(2-y)}{2-y} =-1[/tex]

This is what you get for not doing any maths for almost a year.
 
OH! Jeeeze. I see, lol, Thanks. and, yes. Normally I post in the math homework forums but I think I just clicked on the wrong link and got here. I didn't notice that, sorry.
 
  • #10
ivanetski said:
This forum is more about theoretical discussions.

I thought it was about general math.
 
  • #11
(y-2)/(2-y) = -1 is an equation

(y-2)/(2-y) is not an equation; it's an expression.
 
  • #12
mike_302 said:
and the back of the book gives the final answer to be -1, so I can't do the left side right side stuff

It's -1 for all real numbers y not equal to 2. :wink:
 

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