How do I even start simplifying this expression? {[(x+4)^1/2]-3}/x-5 ?

Its a limits continuation problem with x not equaling 5. What can I do to alter the denominator so that F is continuous at 5?

Question

How do I even start simplifying this expression? {[(x+4)^1/2]-3}/x-5 ?

Its a limits continuation problem with x not equaling 5.  What can I do to alter the denominator so that F is continuous at 5?

rational · Answer

are you trying to evaluate the limit as x->5 ?

amistre64 · Answer

([(x+4)^1/2]-3)/x-5

0/0, try LHop?

anonymous · Answer

Yes im trying to evaluate the limit as x-->5. And Im not using l hop yet

amistre64 · Answer

use a conjugate?

amistre64 · Answer

a table method is to try to evaluate it for values of x closer and closer to x=5, if the lft and right are approaching the same value, then that the limit

anonymous · Answer

Conjugate for the numerator or the denominator?
also  i find it confusing how to use a conjugate if one of the numbers are not under the square root sign.

anonymous · Answer

using foil seems to jumble it up terribly

anonymous · Answer

I cant seem to find a way to make the denominator not equal 0

amistre64 · Answer

by cheating with the wolf, this simplifies to 1/(sqrt(x+4)+3)
which is the conjugate of the top

amistre64 · Answer

(sqrt(x+4) -3)(sqrt(x+4)+3) = x+4-9 = x-5

amistre64 · Answer

so conjugate was indeed the way to approach it

amistre64 · Answer

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

anonymous · Answer

Thank you all very much!

amistre64 · Answer

youre welcome :)