What is this limit? Without using lopital rule

60.

Step-by-step explanation:

(x^2 - 25) / (√(x + 4) - 3).

We rationalise the expression by multiplying top and bottom of the fraction by the complement of the denominator.

That is by (√(x + 4) + 3):

       (x^2 - 25)(√(x + 4) + 3)

=  

     (√(x + 4) - 3)(√(x + 4) + 3)

=   (x + 5)(x - 5)(√(x + 4) + 3)

                (x - 5)

= (x + 5)(√(x + 4) + 3).

The limit as this---> 5

is  (5 + 5)(√(5 + 4) + 3)

= 10 * 6

= 60.