Is Algebraic Equality True? $\frac{x+y}{(x^2+y^2)} = \frac{1}{x+y}$

  • Context: High School 
  • Thread starter Thread starter whatlifeforme
  • Start date Start date
Click For Summary

Discussion Overview

The discussion revolves around the algebraic equality of the expression $\frac{x+y}{(x^2+y^2)} = \frac{1}{x+y}$. Participants are exploring whether this equality holds true, with a focus on algebraic correctness and potential misconceptions.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant questions the algebraic correctness of the equality.
  • Another participant asserts that the equality is not correct.
  • A third participant provides a specific example using numbers, questioning if $\frac{5}{13}$ is equal to $\frac{1}{5}$ as a way to illustrate the original claim.
  • A later reply identifies a common misconception referred to as the "freshman's dream," which involves the incorrect assumption that $(x+y)^2 = (x^2+y^2)$.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus, as there are conflicting views on the correctness of the algebraic equality presented.

Contextual Notes

The discussion highlights potential misunderstandings related to algebraic identities and the specific conditions under which the equality might hold or fail.

whatlifeforme
Messages
218
Reaction score
0
Is \frac{x+y}{(x^2+y^2)} = \frac{1}{x+y}

would that be algebraically correct?
 
Mathematics news on Phys.org
whatlifeforme said:
Is \frac{x+y}{(x^2+y^2)} = \frac{1}{x+y}

would that be algebraically correct?

No, it is not.
 
whatlifeforme,
Would this be correct?

$$ \frac{2 + 3}{2^2 + 3^2} = \frac{1}{2 + 3}$$

More simply, this is asking whether 5/13 is equal to 1/5.
 
And I want to add that your mistake is the so-called "freshman's dream", that is, the incorrect idea that ##(x+y)^2=(x^2+y^2)##, which it does not.
 

Similar threads

Graduate A global version of the implicit function theorem
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad A doubt about the multiplicity of polynomials in two variables
  • · Replies 8 ·
Replies
8
Views
3K
MHB Solving System of Equalities: x^2-y\sqrt xy & y^2-x\sqrt xy =3
  • · Replies 2 ·
Replies
2
Views
1K
High School To calculate the polar unit vectors using rotated coordinates
  • · Replies 1 ·
Replies
1
Views
3K
High School What went wrong with (-x)^2=x^2?
  • · Replies 22 ·
Replies
22
Views
3K
MHB Solve System of 4 Equalities: x+y+z+w=22, xyzw=648
  • · Replies 6 ·
Replies
6
Views
2K
MHB Maximize Σ(x^2+y)(y^2+x))/((x+y-1)^2)
  • · Replies 2 ·
Replies
2
Views
1K
High School Inverse Functions: Why rewrite as y=f(x) ?
  • · Replies 11 ·
Replies
11
Views
2K
MHB Find the possible values of k: x+1/y=y+1/z=z+1/x=k
  • · Replies 2 ·
Replies
2
Views
2K
MHB Challenge Problem #7: Σ(x/(y^3+2))≥1
  • · Replies 2 ·
Replies
2
Views
2K