Question

Simplifique :

É só abrir a imagem






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Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{\dfrac{\left(\dfrac{x^3 - 6x^2 + 11x - 6}{x^2 - 9}.\dfrac{x^2 + 2x - 3}{x^2 - 3x + 2}\right):\left(\dfrac{x^2 + x - 2}{x^2 + 4x + 4}\right)}{\dfrac{2x^2 - 2x}{3x^2 + 3x - 6} - \dfrac{3x^2 + 12x + 12}{2x}}}$

$\mathsf{\dfrac{\left(\dfrac{(x - 1).(x - 2).(x - 3)}{(x + 3).(x - 3)}.\dfrac{(x - 1).(x + 3)}{(x - 1).(x - 2)}\right):\left(\dfrac{(x - 1).(x + 2)}{(x + 2).(x + 2)}\right)}{\dfrac{2x.(x - 1)}{3.(x - 1).(x + 2)} - \dfrac{3.(x + 2).(x + 2)}{2x}}}$

$\mathsf{\dfrac{(x - 1):\left(\dfrac{(x - 1).(x + 2)}{(x + 2).(x + 2)}\right)}{\dfrac{2x.(x - 1)}{3.(x - 1).(x + 2)} - \dfrac{3.(x + 2).(x + 2)}{2x}}}$

$\mathsf{\dfrac{(x - 1):\left(\dfrac{(x - 1)}{(x + 2)}\right)}{\dfrac{2x.(x - 1)}{3.(x - 1).(x + 2)} - \dfrac{3.(x + 2).(x + 2)}{2x}}}$

$\mathsf{\dfrac{(x + 2)}{\dfrac{2x.(x - 1)}{3.(x - 1).(x + 2)} - \dfrac{3.(x + 2).(x + 2)}{2x}}}$

$\mathsf{\dfrac{(x + 2)}{\dfrac{2x}{3.(x + 2)} - \dfrac{3.(x + 2).(x + 2)}{2x}}}$

$\mathsf{\dfrac{(x + 2)}{\dfrac{4x^2 - 9.(x + 2).(x + 2).(x + 2)}{3.(x + 2).2x}}}$

$\mathsf{\dfrac{3.(x + 2).2x.(x + 2)}{4x^2 - 9.(x + 2).(x + 2).(x + 2)}}}$

$\boxed{\boxed{\mathsf{\dfrac{6x(x + 2)^2}{4x^2 - 9(x + 2)^3}}}}}$