Răspuns:
E(x) = (x+1)/(2x-1)
Explicație pas cu pas:
E(x) = [2 +3/(x-1)] : [1- 3x²/(1-x²)]
Conditii:
x-1 ≠ 0 => x ≠ 1
1-x² ≠ 0 => x ≠ -1 ; x ≠ 1
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E(x) = {[2(x-1) +3]/(x-1)} : [(1-x²-3x²)/(1-x²)]
E(x) = [(2x-2+3)/(x-1)] : [(1-4x²)/(1-x²)]
E(x) = (2x+1)/(x-1) · (1-x)(1+x)/[(1-2x)(1+2x)]
Conditii : 1-2x ≠ 0 => x ≠ 1/2
1+2x ≠ 0 => x ≠ -1/2
E(x) = (2x+1) ·(-1)(1+x)/[(1-2x)(1+2x)]
E(x) = (2x+1)(x+1)/[(2x+1)(2x-1)]
E(x) = (x+1)/(2x-1) , ∀ x ∈ R - {± 1 ; ± 1/2}
