Question

Can some one please explain step by step how the following simplifies?

Answer 1

\[(\sqrt{3}+1)/(1-\sqrt{3})\]

Answer 2

according to my math lab the answer is \[-\sqrt{3}+2\]

Answer 3

multiply top and bottom by
\[1+\sqrt{3}\]

Answer 4

why?
Isnt this just a matter of rationalizing

Answer 5

\[\frac{1+\sqrt{3}}{1-\sqrt{3}}\times \frac{1+\sqrt{3}}{1+\sqrt{3}}\]
\[\frac{1+2\sqrt{3}+3}{1-3}\]
\[\frac{4+2\sqrt{3}}{-2}\]
\[-2-\sqrt{3}\]

Answer 6

and how do u know that ur suppose to multiply by the numerator because i have never seen that. We always multiply by the denominator

Answer 7

i think your matlab answer is wrong
and i verified it
http://www.wolframalpha.com/input/?i=%281%2Bsqrt%283%29%29%2F%281-sqrt%283%29%29

Answer 8

i rationalized the denominator, by multiplying top and bottom by the "conjugate" of the denominator, usual trick

Answer 9

so yes, it is just rationalizing the denominator, except in this case when you are done there is no denominator, because the "-2" cancels

Answer 10

Well that is right of my math lab and if we want to rationalize to get the sqrt out of the denominator dont we multiply by the denominator?
you multiplied by the numeraotr

Answer 11

hold the phone

Answer 12

you need to multiply by the conjugate of the denominator to rationalize...

Answer 13

you don't multiply by the denominator, you multiply by the "conjugate" of the denominator.
it just so happened that in this case the conjugate of the denominator happened to be the numerator

Answer 14

What is the defintion of the conjugate term because i must of forgot

Answer 15

just a coincidence of a sort
you would have multiplied by
\[\frac{1+\sqrt{3}}{1+\sqrt{3}}\] irrespective of what the numerator was

Answer 16

the conjugate of (a+b) is (a-b)...

Answer 17

conjugate of
\[a+\sqrt{b}\] is
\[a-\sqrt{b}\]

Answer 18

in real numbers
in complex numbers conjugate of
\[a+bi\] is
\[a-bi\]

Answer 19

and that holds true for anything? because say we want to rationlize the denom of just \[2/\sqrt{3}\]

Answer 20

if we want to rationilize my above example we just multiply by sqrt3

Answer 21

you can think of that denominator as 0+sqrt(3) so the conjugate is 0-sqrt(3).

Answer 22

yea but we dont multiply by -sqrt 3 we just multiply by sqrt 3

Answer 23

if you just have a radical in the denominator, then you can multiply by that

Answer 24

but you need to multiply the numerator by the same expression so the negatives will actually cancell out.

Answer 25

makes no difference if you have for example
\[\frac{3}{\sqrt{5}}\]

Answer 26

but if you have
\[\frac{3}{2+\sqrt{5}}\] you will have to mulitply by
\[\frac{2-\sqrt{5}}{2-\sqrt{5}}\] to get the radical out of the denominator

Answer 27

man i feel fraction retarded somedays
i forgot that who conjugate thing and i just did it last semester

Answer 28

Thanks guys

Answer 29

you will continue to need it, it will rear its ugly head again in calc

Answer 30

yea i figured
i just did alg now in trig