Αντίθετοι παρονομαστές

Να βρεθεί η τιμή του ${\rm A}$: 

${\displaystyle \frac{1}{x-y}}+{\displaystyle \frac{2}{y-x}}+{\displaystyle \frac{3}{x-y}}+{\displaystyle \frac{4}{y-x}}+{\displaystyle \frac{5}{x-y}}+$

$+{\displaystyle \frac{6}{y-x}}+{\displaystyle \frac{7}{x-y}}+{\displaystyle \frac{8}{y-x}}+{\displaystyle \frac{9}{x-y}}+{\displaystyle \frac{10}{y-x}}={\displaystyle \frac{{\rm A}}{x-y}}$.