es 279
es 279
83
punti
Livello 1
1/(x^2 - 1) - 2/(x^2 + 3·x - 4) + 1/(x^2 - 2·x - 3) =
x^2 - 1 = (x + 1)·(x - 1)
x^2 + 3·x - 4 = (x - 1)·(x + 4)
x^2 - 2·x - 3 = (x + 1)·(x - 3)
(x + 1)·(x - 1)·(x + 4)·(x - 3) ≠ 0
x ≠ -4 ∧ x ≠ 3 ∧ x ≠ -1 ∧ x ≠ 1
=
=(1·(x - 3)·(x + 4) - 2·(x + 1)·(x - 3) + 1·(x - 1)·(x + 4))/
/((x + 1)·(x - 1)·(x + 4)·(x - 3))=
=((x^2 + x - 12) - (2·x^2 - 4·x - 6) + (x^2 + 3·x - 4))/
/((x + 1)·(x - 1)·(x + 4)·(x - 3))=
=(8·x - 10)/((x + 1)·(x - 1)·(x + 4)·(x - 3)) =
=2·(4·x - 5)/((x + 1)·(x - 1)·(x + 4)·(x - 3))=
=2·(4·x - 5)/((x - 3)·(x + 4)·(x^2 - 1))
115471
punti
Genius III