Question

rationalize the denominator and simplify. (3+√3)/(3-√3)

Answer 1

I don't get this math >_<

Answer 2

Music, I don't know how to do this. But I pinged @hero and he is very smart.

Answer 3

Multiply the numerator and denominator by (3+√3), then simplify. When it says to 'rationalize the denominator', it means to multiply top and bottom by its conjugate. The conjugate of (3-√3) is (3+√3). Therefore:

\[\frac{3 + \sqrt{3}}{3 - \sqrt{3}} \times \frac{3 + \sqrt{3}}{3 + \sqrt{3}}\]

@music101, can you simplify that?

Answer 4

yeah that's the part I know how to do, Hero

Answer 5

so....1?

Answer 6

that's the answer

Answer 7

thank u hero!

Answer 8

hero is the best and welcome to OpenStudy @music101

Answer 9

thanks ☺

Answer 10

the problem is.... 1 is not an option!!

Answer 11

It's not an option because that's not quite what the correct simplification. Do you have a way of showing what you did?

Answer 12

ugh! dang it! I wish I did. everything's on paper though

Answer 13

I'm interested in knowing how you got 1. My result isn't close to that.

Answer 14

Can you try using the draw button to write it out?

Answer 15

yes. hold on let me double-check something

Answer 16

wait... I was looking at the wrong problem :p

Answer 17

my final answer is 2+√3???

Answer 18

That's correct.

Answer 19

ok thanks ☺

Answer 20

Great recovery

Answer 21

yup :)

Answer 22

the next problem says to solve for x:
√(4x-2) -1=2

Answer 23

I got x= 11/4

Answer 24

that's correct rite?

Answer 25

Correct again

Answer 26

Thanks Hero!

Answer 27

☺

Answer 28

i'm a little stuck on this problem
it's pretty easy but Idk where i'm wrong
can u tell me if my answer is rite?

Answer 29

Which one?

Answer 30

(√(4-3x)/(√3x)=2

Answer 31

I got x= 4/15

Answer 32

& what abt this?
x+2=√(4-x)

Answer 33

\[\frac{\sqrt{4 - 3x}}{\sqrt{3x}} = 2\]\[\sqrt\frac{{4 - 3x}}{{3x}} = 2\]\[\frac{{4 - 3x}}{{3x}} = 4\]\[4 - 3x = 4(3x)\]\[4 - 3x = 12x\]\[4 = 15x\]\[\frac{15}{4} = x\]

Answer 34

I think you just simplified backwards a bit.

Answer 35

ohh :( but I submitted it as my final answer

Answer 36

ok well.....

Answer 37

Whoops, you had it right all along.

Answer 38

4/15 = x is correct.

Answer 39

oh... ok then

Answer 40

\[(x + 2) = \sqrt{4 - x}\]
\[(x + 2)^2 = 4 - x\]

Expand \((x + 2)^2\)

Answer 41

x+2=√(4-x) solve for x?

Answer 42

how do u know which x to solve for?

Answer 43

so.. x^2+4x+4 rite?

Answer 44

Okay good so you have

\[x^2 + 4x + 4 = 4 - x\]

Anytime you see that, it means to move everything to one side and create a quadratic equation.

Answer 45

@music101, did you go offline?

Answer 46

sorry i'm back