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Did I need to rationalise the denominator?

Hi, I was given this question.

3 / (2root2 - 1) - 6 / (2root2)

I rationalised the denominators and the final answer is 3. I have 2 questions.

1 )Could I have completed this question without rationalising the denominators?

2) By looking at this question first, is there anyway I could of know that the final answer would be a whole number?

Thanks for either answers.

Reply 1

Smaug123

Original post by nicevans1

\frac{3}{2 \sqrt{2}-1}-\frac{6}{2\sqrt{2}}

is not 3, but approximately

-0.48

. I don't see a way to do it without manipulating the denominators, though.

Reply 2

brianeverit

Original post by nicevans1

You will have to rationalise denominators at some point.
eg.

\frac{3}{2\sqrt2-1}-\frac{6}{2\sqrt2}=\frac{3\sqrt2-3(2\sqrt2-1)}{\sqrt2(2\sqrt2-1)}=\frac{3(1-\sqrt2)}{4-\sqrt2}

Then at this point you would rationalise the denominator.
The alternative is to rationalise first which is probably the easier method.
And no, you cannot anticipate a whole number answer because it isn't.

Reply 3

nicevans1

Thanks for the replies.

I made a mistake with my equation or "how I wrote it". The denominators are the square root of 2 then minus 1 and the other one is the square root of 2.

Anyway this equation will definitely equal 3... lol

1) So just to confirm in one way or another you would have to rationalise the denominator at some point?

2) You could not tell just from looking at this "new" equation that it would equal a whole number?

Thanks again

Reply 4

TenOfThem

Original post by nicevans1

You would need to add the fractions giving something which factorises and cancels

No rationalising needed

(edited 9 years ago)

Reply 5

nicevans1

Hi thanks for the reply.

does this not contradict the reply of the other poster that at somepoint you need to rationalise the denominator?

Reply 6

TenOfThem

Original post by nicevans1

Hi thanks for the reply.

does this not contradict the reply of the other poster that at somepoint you need to rationalise the denominator?

You changed the question after the previous poster said that

Reply 7

nicevans1

Yes im waiting for someone to respond to my changed question. Your answer was to the original question, was it not?

Reply 8

TenOfThem

Original post by nicevans1

Yes im waiting for someone to respond to my changed question. Your answer was to the original question, was it not?

No I just quoted the original post

I posted after you changed the question ... I was answering the correct question ... The one where the answer is rational so there is no need to rationalise the denominator

Please use the reply button

(edited 9 years ago)

Reply 9

nicevans1

ok. I would like to change my post/question one more time... If I had NEVER told you the answer would of been 3 (a rational number)...

1) would you of then had to reationalise the denominator?

Many thanks.

p.s when you say the reply button? there are 3. I automatically go to quick reply...

Reply 10

davros

Original post by nicevans1

"would have" not "would of" :smile:

No, you don't need to rationalise the denominator(s).

The Reply button is the first one you come to, the one next to the double quote (") icon - it causes the previous poster's text to be quoted so they can see you have replied to them (as I have done here) :smile:

Reply 11

TenOfThem

Original post by nicevans1

No I would not have rationalised .... I would add the fractions and the answer would have factorised and cancelled

The reply button that is on the post you with to reply to .... This tells the poster that you have replied

Reply 12

nicevans1

Original post by davros

"would have" not "would of" :smile:

Original post by TenOfThem

lol - i love learning new things :-)

ok - but i'm guessing it's easier to rationalise the denominator as this question was one that was given in the section in my book about the rationalising?

And just so i know, is this the right way to do it your way and to make the denominators the same?

3(root2) - 6(root2-1) / root2-1 * root2

3root2 -6root2-6 / 2-root2

Right so far and if so where next?

Reply 13

davros

Original post by nicevans1

You really ought to use more brackets if you're not going to use Latex!

Your -6 at the end of the numerator should be a +6 - it comes from -6 x -1.

You can then simplify the numerator by combining the first two terms.

Reply 14

TenOfThem

Original post by nicevans1

First -6 x -1 is 6 not -6

Second ... How many root2 do you have

Reply 15

nicevans1

Original post by davros

Your -6 at the end of the numerator should be a +6 - it comes from -6 x -1.

Rushing.!!!

Original post by TenOfThem

Second ... How many root2 do you have

Where about? Ive continued below...

Question is...
3/(root2-1) - 6/(root2)

3(root2) - 6(root2-1) / (root2-1 * root2)

(3*root2 - 6root2+6) / ( 2-root2)

(6-3*root2) / (2-root2)

Good so far? Im unsure from here. Another clue maybe?

Reply 16

TenOfThem

Original post by nicevans1

Rushing.!!!

Where about? Ive continued below...

Question is...
3/(root2-1) - 6/(root2)

3(root2) - 6(root2-1) / (root2-1 * root2)

(3*root2 - 6root2+6) / ( 2-root2)

(6-3*root2) / (2-root2)

Good so far? Im unsure from here. Another clue maybe?