Question #b8966

Question

1123 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-08-31T03:38:03

$lim_(xrarr1)(1/x^2-1)/(x-1)=-2$

$L=lim_(xrarr1)(1/x^2-1)/(x-1)$

Multiply the numerator and denominator by $x^2$ to clear the fraction in the numerator:

$L=lim_(xrarr1)(x^2(1/x^2-1))/(x^2(x-1))=lim_(xrarr1)(1-x^2)/(x^2(x-1))$

Factor the numerator as a difference of squares:

$L=lim_(xrarr1)((1+x)(1-x))/(x^2(x-1))$

Note that $1-x=-(x-1)$ :

$L=lim_(xrarr1)(-(x+1)(x-1))/(x^2(x-1))=lim_(xrarr1)(-(x+1))/x^2=(-(1+1))/1^2=-2$