Did I need to rationalise the denominator?

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nicevans1
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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.
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Smaug123
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(Original post by nicevans1)
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.
\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.
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brianeverit
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(Original post by nicevans1)
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.
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.
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nicevans1
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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
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TenOfThem
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(Original post by nicevans1)
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.
You would need to add the fractions giving something which factorises and cancels

No rationalising needed
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nicevans1
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Hi thanks for the reply.

does this not contradict the reply of the other poster that at somepoint you need to rationalise the denominator?
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TenOfThem
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(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
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nicevans1
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Yes im waiting for someone to respond to my changed question. Your answer was to the original question, was it not?
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TenOfThem
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(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
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nicevans1
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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...
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davros
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(Original post by 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...
"would have" not "would of"

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)
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TenOfThem
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(Original post by 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...
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
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nicevans1
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(Original post by davros)
"would have" not "would of"

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)
(Original post by TenOfThem)
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
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?
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davros
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(Original post by nicevans1)
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?
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.
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TenOfThem
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(Original post by nicevans1)
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?
First -6 x -1 is 6 not -6

Second ... How many root2 do you have
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nicevans1
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(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?
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TenOfThem
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(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?
Factorise the numerator
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nicevans1
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(Original post by TenOfThem)
Factorise the numerator
Thanks. So easy now....
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