Question

Could someone help with this limit problem?

lim x-->1 of
((sqrt(6-x))-2)/((sqrt(10-x)-3))

I tried to rationalize the denominator and numerator but it didn't work!

Answer 1

(√(6-x)-2)/(√(10-x)-3)

(√(6-x)-2)(√(10-x)+3)
-----------------------
(√(10-x)-3)(√(10-x)+3)

(√(6-x)-2)(√(10-x)+3)
----------------------
10-x-9

as x->1, that is

(6√5 - 12)/±0

undefined