Question

calculate lim x^2-1/x^2-x as x approahces to 1.

Answer 1

(x^2-1)/(x^2-x)


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


((x+1)(x-1))/(x(x-1))


(x+1)/x



Now plug in x = 1 to get


(x+1)/x

(1+1)/1

2/1

2


So the answer is 2

Answer 2

thanks.

Answer 3

First notice that

\[(x^2-1)/(x^2 - x) = (x-1)(x+1)/x.(x-1) = (x+1)/x\]

Hence the limit

\[ \lim_{x -> 1} (x^2-1)/(x^2 - x) = \lim_{x->1} (x+1)/x\ = 2/1 =2.\]

Answer 4

thanks