Exercício sobre álgebra elementar

(PUC) Simplificando a expressão $\phantom{X}\dfrac{\;2(x\,-\,2)(x\,-\,3)^3\,-\,3(x\,-\,2)^2(x\,-\,3)^2\;}{(x\,-\,3)^6}\phantom{X}$ obtém-se:

$\,\dfrac{\;x(x\,-\,2)\;}{(x\,-\,3)^3}\,$

$\,\dfrac{\;x(2\,-\,x)\;}{(x\,-\,3)^3}\,$

$\,\dfrac{\;x(x\,-\,2)\;}{(x\,-\,3)^4}\,$

$\,\dfrac{\;x(2\,-\,x)\;}{(x\,-\,3)^4}\,$

$\,\dfrac{\;5x(x\,-\,2)\;}{(x\,-\,3)^4}\,$

Observação: supor x ≠ 3

resposta: (D)
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