Question

Arătați că [6x-12/(x-2)²-5x-15/(x-3)²]:2/x²-5x+6=x-8/2,x aparține R\{2;3}.

Answer 1

{6 x - 12/(x - 2)^2 - 5 x - 15/(x - 3)^2:2/x^2 - 5 x + 6 = (x - 8)/2, x, R/({2, 3})}

{x - 15/(x - 3)^2 - 12/(x - 2)^2:-5 x + 6 + 2/x^2 = x - 4, x, {R/2, R/3}}

Answer 2

Răspuns:

Explicație pas cu pas:

x²-5x+6=x²-2x-3x+6=x(x-2)-3(x-2)=(x-2)(x-3)

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[ ( 6x-12)/(x-2)² - (5x-15)/(x-3)²] : 2/(x²-5x+6) =

= [6(x-2)/)(x-2)² - 5(x-3)/(x-3)²] : 2/(x-2)(x-3) =

= [ 6/(x-2) - 5/(x-3)] × (x-2)(x-3)/2 =

= [6(x-3)-5(x-2)]/(x-2)(x-3)  × (x-2)(x-3)/2 =

= (6x-18-5x+10)/2 =

= (x-8)/2; x ∈ R \{2; 3}  → cctd