lim x=~ (√x+1-√x+3)(√4x+1) =...

= Lim (√x+1-√x+3)(√4x+1)
   x⇒∞
= Lim (√x/x+1/x - √x/x+3/x)(√4x/x+1/x)
   x⇒∞
= (√1+0 - √1+0) (4+0)
= 0 (4)
= 0

Lim (√(x + 1) - √(x + 3))√(4x + 1)
= Lim √(x + 1)(4x + 1) - √(x + 3)(4x + 1)
= Lim √(4x^2 + 5x + 1) - √(4x^2 + 13x + 3)
a = 4, b = 5, c = 1, p = 4, q = 13, r = 3
= (b - q)/(2√a)
= (5 - 13)/(2√4)
= -8/4
= -2