How would i rationalize 6/ 3+i

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How would i rationalize 6/ 3+i

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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multiply by the conjugate
multiply by 1 using the conjugate*
* top n bottom by 3-i

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Other answers:

So 9i?
6(3-i) / (3+i)(3-i)
Is that all that I have to do? I'm not really sure how to do these sorts of problems
You need to multiply out the brackets and simplify if possible
Just like normal except you have i's to deal with...
6(3-i)? Wouldn't the bottom cancel itself out?
It is a kind of trick to get rid of the i on the bottom.....
Similar to how you get rid of a rdical, same sort of idea...
So confused
Multiply it out and you will see...
9-i/9
which you could divide 9 by 9 to get one, so -i?
6(3-i) is 18-6i Where do you get 9-i from?
Oh wow opps. haha I added.
Ok, now what do you get for the bottom?
9?
You have (3+i)(3-i) Tell me how it comes to 9
You multiply and the +i and -i cancel out? i'm really sorry, this is new to me haha
(3+i)(3-i) is 3*3 + 3*i -3*i - i^2 (using FOIL?)
So the 3i's cancel out and leave 9-i^2 So what is i^2 ?
-1
Right, so what is the bottom ( hint-it is not 9)
8?
9-(-1)
10
Ok so finally you have 18-6i/10 which you can divide by 2 to get 9-3i/5 as a final answer.
So, procedure for these is *by conjugate top and bottom then simplify
thank you so much!!!
ur welcome

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