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 October 29th, 2017, 04:25 AM #1 Newbie   Joined: Oct 2017 From: UK Posts: 2 Thanks: 0 Please simplify this Hello This question is from Engineering Mathematics 5th Ed, Further Problems F.2 Question 2 $\displaystyle (x^2-1)^2*(x+1)^{1/2}/(x-1)^{3/2}$ the answer at the back of the book is given as $\displaystyle (x+1)^2(x^2-1)^{1/2}$ I would like to see the working Many thanks
October 29th, 2017, 09:57 AM   #2
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 Originally Posted by Bozza Hello This question is from Engineering Mathematics 5th Ed, Further Problems F.2 Question 2 $\displaystyle (x^2-1)^2*(x+1)^{1/2}/(x-1)^{3/2}$ the answer at the back of the book is given as $\displaystyle (x+1)^2(x^2-1)^{1/2}$ I would like to see the working Many thanks
Please post what you have been able to do. That will allow us to help you better.

Hint: How do you factor $\displaystyle x^2 - 1$?

-Dan

October 29th, 2017, 10:00 AM   #3
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Quote:
 Originally Posted by Bozza Hello This question is from Engineering Mathematics 5th Ed, Further Problems F.2 Question 2 $\displaystyle (x^2-1)^2*(x+1)^{1/2}/(x-1)^{3/2}$ the answer at the back of the book is given as $\displaystyle (x+1)^2(x^2-1)^{1/2}$ I would like to see the working Many thanks
$\dfrac{(x^2 - 1)^2(x + 1)^{1/2}}{(x - 1)^{3/2}} = \dfrac{\{(x + 1)(x - 1)\}^2 * (x + 1)^{1/2}}{(x - 1)^{3/2}} = \dfrac{(x + 1)^2(x - 1)^2 (x + 1)^{1/2}}{(x - 1)^{3/2}} =$

$\dfrac{(x + 1)^2(x - 1)^{4/2}(x + 1)^{1/2}}{(x - 1)^{3/2}} = (x + 1)^2(x - 1)^{1/2}(x + 1)^{1/2} = (x + 1)^2\{(x - 1)(x + 1)\}^{1/2} =$

$(x + 1)^2(x^2 - 1)^{1/2}.$

I suspect that you got the answer $(x + 1)^{5/2}(x - 1)^{1/2}$,

which is also correct.

Last edited by JeffM1; October 29th, 2017 at 10:04 AM.

 October 30th, 2017, 05:20 AM #4 Newbie   Joined: Oct 2017 From: UK Posts: 2 Thanks: 0 Thanks very much to the both of you. I hadn't considered factoring x^2-1. This should help with some other questions too.

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