Question

Evaluate the given limit: lim x->3 ((x-3)/(sqrt(x) - sqrt(6-x)))

(NO l'hospital)

Answer 1

\[\frac{ x-3 }{ \sqrt{x}-\sqrt{6-x} }*\frac{ \sqrt{x} +\sqrt{6-x}}{ \sqrt{x}+\sqrt{6-x} }\]

Answer 2

(a-b)(a+b)=a^2-b^2

Answer 3

this will be applicable for denominator

Answer 4

\[\frac{ (x-3)(\sqrt{x}+\sqrt{6-x}) }{ (\sqrt{x})^2 -(\sqrt{6-x})^2}\]

Answer 5

\[\frac{ (x-3) *(\sqrt{x}+\sqrt{6-x}}{ x-6+x }\]

Answer 6

no x isn't canceling
in denominator we have 2x-6=2(x-3)
cancel x-3
we are left with (root(x)+root(6-x))/2 now substitute directly
the result is root(3)

Answer 7

Oops, misread that as \(x-x\) for some reason... Thanks for pointing it out!

Answer 8

Welcome!^_^