Vamos lá.
a)
1/a + 1/(2a - 1) - 1/(2a + 1) - 2/(4a^2 - 1) =
1/(2a - 1) - 1/(2a + 1) - 2/((2a - 1)*(2a + 1) =
(2a + 1 - 2a + 1 - 2)/(2a - 1)*(2a + 1) = 0
1/a + 1/(2a - 1) - 1/(2a + 1) - 2/(4a^2 - 1) = 1/a
b)
(3 - x) + x^2/(3 + x) =
(3 - x)*(3 + x)/(3 + x) + x^2/(3 + x) =
(9 - x^2 + x^2)/(x + 3) = 9/(x + 3)
c)
(x + 3a)/(2x - 6a) + (x - 3a)/(2x + 6a) - (6ax)/(x^2 - 9a^2) = (x - 3a)/(3a + x)
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Vamos lá.
a)
1/a + 1/(2a - 1) - 1/(2a + 1) - 2/(4a^2 - 1) =
1/(2a - 1) - 1/(2a + 1) - 2/((2a - 1)*(2a + 1) =
(2a + 1 - 2a + 1 - 2)/(2a - 1)*(2a + 1) = 0
1/a + 1/(2a - 1) - 1/(2a + 1) - 2/(4a^2 - 1) = 1/a
b)
(3 - x) + x^2/(3 + x) =
(3 - x)*(3 + x)/(3 + x) + x^2/(3 + x) =
(9 - x^2 + x^2)/(x + 3) = 9/(x + 3)
c)
(x + 3a)/(2x - 6a) + (x - 3a)/(2x + 6a) - (6ax)/(x^2 - 9a^2) = (x - 3a)/(3a + x)