Explain what is wrong with the following argument - be specific.

Question

lim x→2 x^2 +3x-10/x^2-x-2 = (x-2)(x+5)/(x-2)(x+1) = x+5/x+1 = 2+5/2+1 = 7/3

Answer 1

x^2+3x -10= (x+5)(x-2)

x^2 -x -2 = (x-2)(x+1)

divide top factors by bottom and the (x-2) factor cancels out, leaving

(x+5)/(x+1)

plug in x=2

(2+5)/(2+1) = 7/3 = limit as x approaches 2

nothing wrong with the argument

right conclusion, right calculation, unless there's some technical math reason to be critical