Question

help!!

Answer 1

please put in evidence a power x^2 into the radicand

Answer 2

after some simplification we can write:
\[f(x)=\frac{ x \sqrt{1+24/x ^{2}} -5}{ x(1-1/x) }\]

Answer 3

that's right!

Answer 4

if you calculate x(1-1/x), you get:
x-1, are you agree?

Answer 5

ok!

Answer 6

please put in evidence x at the numerator, the write your answer

Answer 7

\[x(\sqrt{1+24/x ^{2}}+...)\]
please continue!

Answer 8

after you put x in evidence at numerator you will get:
\[x(\sqrt{1+\frac{ 24 }{ x ^{2} }}-\frac{ 5 }{ x })\]
are you agree?

Answer 9

now you can simplify the x at numerator with the x at denominator and you will get the subsequent expression:
\[\frac{ \sqrt{1+24/x ^{2}}-5/x }{ (1-1/x) }\]
are you agree?

Answer 10

ok! nevertheless I have made an error, I was convinced that you had to calculate a limit when x--->+infinity, sorry, I retry

Answer 11

I got, multiply both numerator and denominator by this quantity:
\[(\sqrt{x ^{2}+24}+5)\]

Answer 12

please, you will get the subsequent expression:
\[\frac{ (\sqrt{x ^{2}+24}-5 )(\sqrt{x ^{2}+24}+5)}{ (x-1)(\sqrt{x ^{2}+24}+5) }\]
are you agree?

Answer 13

now calculate the multiplication at the numerator, it's very simple because the result is a diference between two square quantities. You will get this expression:

Answer 14

\[\frac{ x ^{2}-1 }{ (x-1)(\sqrt{x ^{2}+24}+5) }\]
are you agree?

Answer 15

@wade123

Answer 16

ok! now keep in mind that (x^2-1)=(x-1)(x+1) please substitute at numerator
(x-1)(x+1) in place of x^2-1

Answer 17

that's right!

Answer 18

ok! now insert please x=1 in your resultant expression, and write your result

Answer 19

that's right again, congratulations!!!

Answer 20

thank you!