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# Further mathematics (GCSE) Urgent help is required. Watch

1. Expand and simplify:
2x^1/2(x^1/2-x^-1/2)
I am not very sure how to solve this.
Thank you in advance fellow TSRians.
2. (Original post by Wolfram Alpha)
Expand and simplify:
2x^1/2(x^1/2-x^-1/2)
I am not very sure how to solve this.
Thank you in advance fellow TSRians.
Expand as you normally would.

And use the fact that .

Post your working if you get stuck.
3. add the outer power by the inner power of each while putting a 2 in front , 2x1X^1/2+1/2 - 2x1X^1/2+(-1/2) and simplify it to 2X-2
4. (Original post by notnek)
Expand as you normally would.

And use the fact that .

Post your working if you get stuck.
I multiplied 2x^1/2 by x^1/2 which gives 2x. Then 2x^1/2 multiplier by x^-1/2 which gives 2x^0. So would the answer just be 2x + 1?
5. (Original post by Wolfram Alpha)
I multiplied 2x^1/2 by x^1/2 which gives 2x. Then 2x^1/2 multiplier by x^-1/2 which gives 2x^0. So would the answer just be 2x + 1?
is correct.

But it should be instead of . Can you see why?

And
6. (Original post by notnek)
is correct.

But it should be instead of . Can you see why?

And
Ah, I have just noticed the negative sign. So -2x^0 gives -2 rather than zero. Thus the final answer is 2x-2. I thank you for your time. It is much appreciated.
7. (Original post by Wolfram Alpha)
Ah, I have just noticed the negative sign. So -2x^0 gives -2 rather than zero. Thus the final answer is 2x-2. I thank you for your time. It is much appreciated.
Correct
8. (Original post by regan1234567)
add the outer power by the inner power of each while putting a 2 in front , 2x1X^1/2+1/2 - 2x1X^1/2+(-1/2) and simplify it to 2X-2
9. (Original post by notnek)
Correct
I have one more question friend. (3x^1/2 - 2x^-1/2)(2x^1/2 - 3x^-1/2) equals 6x - 13 + 1/6x. Am I correct?
10. (Original post by Wolfram Alpha)
I have one more question friend. (3x^1/2 - 2x^-1/2)(2x^1/2 - 3x^-1/2) equals 6x - 13 + 1/6x. Am I correct?
Nearly but 1/6x is incorrect.

11. (Original post by notnek)
Nearly but 1/6x is incorrect.

I thought 6x^-1 was 1/6x. I am clearly wrong. Could you please enlighten me?
12. (Original post by Wolfram Alpha)
I thought 6x^-1 was 1/6x. I am clearly wrong. Could you please enlighten me?
Both are wrong but It's not clear if 1/6x means or .

Explanation :

You know that

So

It will be useful for you to become familiar with this rule :

E.g. or .
13. (Original post by notnek)
Both are wrong but It's not clear if 1/6x means or .

Explanation :

You know that

So

It will be useful for you to become familiar with this rule :

E.g. or .
Ah, I see! I was aware of that rule but I suppose I got confused when applying it. Mhmm, thanks for your help again.

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