Problem stating: if A = x - 1/x, find A - 1/A

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Discussion Overview

The discussion revolves around a mathematical problem where participants are tasked with finding the expression A - 1/A given that A = x - 1/x. The scope includes mathematical reasoning and problem-solving strategies.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant expresses confusion about how to approach the problem and seeks insight.
  • Another participant reiterates the definition of A and begins to explore the expression for 1/A.
  • A third participant requests clarification on the logic behind the problem, indicating a lack of familiarity with similar math problems.
  • A fourth participant suggests simplifying the fractions and provides a step-by-step approach to rewriting A and 1/A, including finding a common denominator.
  • A fifth participant acknowledges understanding after receiving help.

Areas of Agreement / Disagreement

Participants do not appear to have reached a consensus on the solution process, but there is a collaborative effort to clarify the steps involved in solving the problem.

Contextual Notes

Some participants may have missing assumptions regarding their familiarity with algebraic manipulation, and there are unresolved steps in the simplification process.

Who May Find This Useful

Students or individuals looking for assistance with algebraic expressions and simplification techniques may find this discussion beneficial.

trip7
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I have a math problem stating:
if A = x - 1/x, find A - 1/A

I have no clue as to how to solve this. Any insight would be greatly appreciated.
 
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You have that:

A = x - 1/x
1/A = 1/(x - 1/x)

Then A - 1/A = what?
 
Muzza:
Im sure this is easy but I am completely missing the logic. I haven't done this kind of math in a while and hoping you could explain the logic.
 
Just simplify the fractions...

[tex]A = x - \frac {1}{x} = \frac{x^2 - 1}{x}[/tex]

[tex]So, ~ 1/A = \frac {x} {x^2 -1}[/tex]

[tex]So, ~A - 1/A = \frac{x^2 - 1}{x} - \frac {x} {x^2 -1}[/tex]

Take the lcm and simplify.
 
Thanks Gokul43201:

Ok, now I got it.
 

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