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

  • Thread starter mike_302
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In summary, the poster is struggling to find the steps to prove that (y-2)/(2-y)=-1. The conversation highlights the use of the conjugate of the denominator to simplify the expression and the reminder to post homework questions in the appropriate forum. The final answer is -1 for all real numbers y not equal to 2.
  • #1
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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  • #2
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.
 
  • #3
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]
 
  • #4
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
 
  • #5
ahh, yes, I see your second post now . That does seem to be better. Thanks
 
  • #6
so basically what I do in your second post is I multiply the bottom and top by the conjugate of the denominator?
 
  • #7
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.
 
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  • #8
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.
 
  • #9
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:
 

1. What is the significance of the number -1 in this equation?

In mathematics, the number -1 is known as the additive inverse or the opposite of 1. This means that when added to 1, it results in a sum of 0. In other words, -1 is the number that, when added to any number, yields the additive identity of 0.

2. How can an equation equal -1?

An equation can equal -1 when two or more terms with opposite signs are involved. For example, the equation 3x - 4 = -1 has a term with a positive coefficient (3x) and a term with a negative coefficient (-4), resulting in a net value of -1.

3. Can -1 be the solution to any equation?

Yes, -1 can be the solution to certain equations, such as quadratic equations, linear equations, or even complex equations. However, it is not always the case and depends on the specific variables and constants involved in the equation.

4. Why is -1 often used in equations?

-1 is often used in equations because it is a commonly used constant that has specific properties, such as being the additive inverse of 1 and the multiplicative inverse of -1. This makes it a useful tool for balancing equations and solving for unknown variables.

5. How does the value of -1 affect the overall solution of an equation?

The value of -1 plays a crucial role in the overall solution of an equation. It can be used as a constant to balance the equation or as a solution to the equation itself. It can also affect the behavior of the equation, such as changing its slope or intercept when graphed. Overall, -1 has a significant impact on the solution and interpretation of an equation.

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