Question

limit question. will give medal.

lim (x-1) / [(sqrt of 2x-1) -1]
x-->1

The answer is 1. I have the work as well. But, I don't know how they got to the last step. so basically taking the conjugate of the denominator and putting it at the top. I dont understand how they simplified the denominator to cancel out common terms.

Answer 1

@phi @bibby @PaxPolaris @iambatman @myininaya

Answer 2

grabbing something to eat, will be back in 20 mins. please help break up the steps after conjugating!

Answer 3

rationalize the bottom

Answer 4

oh so you know to multiply by bottom's conjugate on top and bottom

Answer 5

\[\frac{x-1}{\sqrt{2x-1}-1} \cdot \frac{\sqrt{2x-1}+1}{\sqrt{2x-1}+1} =\frac{(x-1)(\sqrt{2x-1}+1)}{(2x-1)-1}\]

Answer 6

2x -2 when setting x =1, would give 0 though

Answer 7

hey! @freckles @jdoe0001

Answer 8

I understand up to that point @freckles ...but after that the denominator becomes (2x-1) -1....which further simplifies to 2(x-1)....I dont get that part

Answer 9

i left you to simplify the bottom there

Answer 10

and then factor the bottom to see a common factor that is on both top and bottom

Answer 11

I don't get how the denominator gets to 2(x-1)

Answer 12

yes, the common factor is suppose to be (x-1)...but I dont get it

Answer 13

2x-1-1
2x-2
2(x-1)

Answer 14

omgd you are right!

Answer 15

are you saying you don't get how (sqrt(2x-1)-1)*(sqrt(2x-1)+1)=2x-1-1?

Answer 16

oh ok

Answer 17

no i didnt get that simplifying part...thankyou! I get how the answer is one now!

Answer 18

yeah 1 is correct :p