Sum and difference of squares

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Question from Anne, a student:

Se x e y são números reais distintos, então:
a) (x² + y²) / (x - y) = x + y
b) (x² + y²) / (x - y) = x - y
c) (x² - y²) / (x - y) = x + y
d) (x² - y²) / (x - y) = x - y
e) Nenhuma das alternativas anteriores é verdadeira.

Hi Anne,

\[\frac{a}{x - y} = x + y\]

then

\[(x - y) \frac{a}{x - y} =(x - y)(x + y)\]

\[a = (x - y)(x + y).\]

Expand the right side. Which of a), b), c) and d) is true?

Harley

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