Răspuns:
[tex]E(x)=\frac{x+1}{x+2}[/tex]
Explicație pas cu pas:
E(x) = [(2x-1)/(x²-4) - 3/(2-x)] : 5/(x-2)
= [(2x-1)/(x-2)(x+2) - 3/-(x-2)] : 5/(x - 2)
= [(2x-1)/(x-2)(x+2) + 3/(x-2)] : 5/(x - 2)
= [2x-1 + 3(x+2)]/(x-2)(x+2) × (x-2)/5
simplificam (x+2) si (x-2)
= (2x - 1 + 3x + 6)/5(x+2)
= (5x + 5)/5(x+2)
= 5(x+1)/5(x+2)
= (x+1)/(x+2)
