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x -> ∞
= Lim (√(x-5) - √(x+4)) × ((√(x-5) + √(x+4))/(√(x-5) + √(x+4))
x -> ∞
= Lim (((x-5) - (x+4))/(√(x-5) + √(x+4))
x -> ∞
= Lim (-9)/(√(x-5) + √(x+4))
x -> ∞
= Lim (-9)/(√(x-5) + √(x+4)) × ((1/x)/(1/x))
x -> ∞
= (0)/(√(1-0) + √(1+0))
= (0)/(√(1) + √(1))
= (0)/(1+1)
= 0/2
= 0