Question

salut am aceasta problema x^2+6x/x-2 derivat si derivez si mai calculez dupa derivata si nu mai stiu ce sa fac ca sa imi dea​ (x-6)(x+2)/(x-2)^2

Answer 1

$\it \Big(\dfrac{x^2-6x}{x-2}\Big)'=\dfrac{(2x+6)(x-2)-(x^2+6x)}{(x-2)^2}=\dfrac{2x^2-4x+6x-12-x^2-6x}{(x-2)^2}=\\ \\ \\ =\dfrac{x^2-4x-12}{(x-2)^2}=\dfrac{x^2-6x+2x-12}{(x-2)^2}=\dfrac{x(x-6)+2(x-6)}{(x-2)^2}=\dfrac{(x-6)(x+2)}{(x-2)^2}$