Limit.........?

limit of ((4/x-4/3)/(x-3)) as x approaches 3


i got 4/9 but the answers is -4/9?


why is it negative?|||Because if you use the De L' Ho%26gt;pital rule, you have to find the derivative of 4/x, which is -4/x^2. (You have to use the rule, because the fraction ((4/x-4/3)/(x-3)) becomes a 0/0 when you replace x with 3).|||lt (4/x-4/3)/(x-3)


x-%26gt;3





= lt (4/x-4/3)/(x-3)


x-%26gt;3





= lt (12-4x)/3x(x-3)


x-%26gt;3





= lt 4(3-x)/3x(x-3)


x-%26gt;3





= lt - 4(x-3)/3x(x-3)


x-%26gt;3








= lt - 4/3x


x-%26gt;3





= -4/9


===|||differentiating


-4/x^2/1


allowingthe limit


=-4/9|||lim [ (4/x) - (4/3) ] / (x-3)





= lim [ (4/x) (3/3) - (4/3) (x/x) ] / (x-3)





=lim [ (12/3x) -(4x/3x) / (x-3)





=lim [ (12-4x) / 3x ] / (x-3)





=lim [ (4) (3-x) / 3x ] / (x-3)





=lim [ (4) (-1) / 3x





=lim [ (-4)/ 3x ] = -4/9


x-%26gt;3