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

Question

lim x→2 (x² +3x-10)/(x²-x-2) = (x-2)(x+5)/(x-2)(x+1) = x+5/x+1 = 2+5/2+1 = 7/3

Answer 1

the argument's conclusion is correct

each line correct, if interpreted with some missing parentheses

maybe you're asking what tiny technical move in the argument isn't kosher or PC enough?

maybe "what is wrong" refers to lack of parentheses in the part x+5/x+1 which with PEMDAS means x+(5/x)+1, not (x+5)/(x+1)

then there's the missing "lim as x approaches 2" in each line, instead of just at the beginning

so 2+5/2+1 would = 11/2 not 7/3, as written

use a graphing calculator to graph (x^2+3x-10)/(x^2-x-2)

also graph (x+5)/(x+2)

or maybe more likely, the instructor or textbook's problem just wants to see you use L'Hopital's rule with derivatives of numerator and denominator to get

(2x+3)/(2x-1)

then plug 2 in to get

((2(2)+3)/(2(2)-1)=

(4+3)/(4-1)

= 7/3