# Question #b8966

##### 1 Answer

Aug 31, 2017

#### Explanation:

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

Multiply the numerator and denominator by

#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

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