Find the limit if it exists If the limit has a numerical val

Find the limit, if it exists. If the limit has a numerical value, give that value. If it can be determined that the limit is infinate , indicate that. If the limit does not exist write DNE and give a reason for your answer.

lim x^2 +4x-5 (numerator) over 2x^2-7x+5 (denominator)

x--->1

Solution

lim   x--> 1   (x^2 +4x-5)/ (2x^2-7x+5)
=lim x--> 1 (x^2+5x-x-5)/(2x^2-2x-5x+5
=lim x--> 1 (x(x+5) -1(x+5))/(2x (x-1)-5(x-1))
lim x-->1 {(x+5)(x-1)}/{(2x-5)(x-1)}
lim x-->1 (x+5)/(2x-5)
now put the value x=1
Limit = (1+5)/(2*1-5)
      = 6/(-3)
      = -2
Answer: -2