Răspuns:
Explicație pas cu pas:
a)
numaratorul fractei
a/(a - 1) - (a + 1)/a = [a^2 - (a + 1)(a - 1)]/a(a - 1) = [a^2 - (a^2 - 1)]/a(a - 1) =
(a^2 - a^2 +1)/a(a -1) = 1/a(a - 1)
numitorul fractiei
a/(a + 1) - (a - 1)/a = [a^2 - (a + 1)(a - 1)]/a(a + 1) = [a^2 - (a^2 - 1)]/a(a + 1) =
(a^2 - a^2 + 1)/a(a + 1) = 1/a(a + 1)
fractia
1/a(a - 1) : 1/a(a + 1) = a(a + 1)/a(a - 1) = (a + 1)/(a - 1)
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b)
a/b + b/a = (a^2 + b^2)/ab
(a + b)/(a - b) + (a - b)/(a + b) = [(a + b)^2 + (a - b)^2]/(a - b)(a + b) =
(a^2 + 2ab + b^2 + a^2 - 2ab + b^2)/(a - b)(a + b) = (2a^2 + 2b^2)/(a +b)(a - b) =
2(a^2 + b^2)/(a + b)(a - b)
ecuatia devine
2(a^2 + b^2)/(a + b)(a - b) : (a^2 + b^2)/ab x (a + b)/2ab
= 2(a^2 + b^2)/(a + b)(a - b) x ab/(a^2 + b^2) x (a + b)/2ab
= 1/(a - b)
