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

[whatlifeforme]

Is \frac{x+y}{(x^2+y^2)} = \frac{1}{x+y}

would that be algebraically correct?

 

[gmax137]

Is \frac{x+y}{(x^2+y^2)} = \frac{1}{x+y}

would that be algebraically correct?

No, it is not.

 

[Mark44]

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.

 

[Vorde]

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.