Could someone please help me with this problem I need to use the included theorem

Theorex 5.1.13 Ler f: D - RR and g: D- of and ler c be an accumulation Then X* C point of D. If lim f ( x ) = L , lim g (x ) = M, and KEIR, lim (f+g) (x) = 1+H, lim ( fg) (x) = LM. and lim (KF ) ( x ) = KL X+C Furthermore, if g(x) * 0 for all X ED and M $ O, Then lim ( # )( x ) = = Determine the following limits lim X+ 4 lim x3+ 4 by The quotient formula of Theorem 5.1.13 lim since lim * + 1 $ 0 and X"+1 0 for all x X4 1 in domain of x + 1 13 + 4 12 +1 lim x4- 5x+4 Since x2- 6*+ 5 = (x-1) ( x- 5) = 0 when * = 1, 5, x1 x2- 6x+ 5 before applying Theorem 5. 1. 13, we simplify The quotient. x - 5 x+4 (*-1) ( x-4 ) X - 4 = x 2- 6 x+5 ( x - 1) ( x -5 ) x - 5 Since lim x- 5 = 1-5 =-4 + 0 Then we X-$1 Can apply the quotient formula of Theorem 5. 1. 13 lim x - 5x+4 - lim X- 4 = 1w * 2-6*+5 x41 x - 5 7- 5 Is it OK That at xos x-5 =0? lim VX - 1 X - 1 Since x-1 : 0 when x=1, before applying theoren 5.1.13, we simplify the quotient. JX - 1 V X - 1