Evaluate the limit or state that it does not exist. (If an answer does not exist

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-9 lim_(x->1) (18/(1-x)-36/(1-x^2)) Indeterminate form of type infinity - infinity, write 18/(1-x)-36/(1-x^2) as -(18 x)/(x^2+x): = lim_(x->1) -(18 x)/(x^2+x) Factor out constants: = -18 (lim_(x->1) x/(x^2+x)) The limit of a quotient is the quotient of the limits: = -(18 (lim_(x->1) x))/(lim_(x->1) (x^2+x)) The limit of x as x approaches 1 is 1: = -18/(lim_(x->1) (x^2+x)) The limit of x^2+x as x approaches 1 is 2: Answer: | | = -9

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