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October 29th, 2017, 05:25 AM   #1
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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
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October 29th, 2017, 10:57 AM   #2
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Quote:
Originally Posted by Bozza View Post
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
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October 29th, 2017, 11:00 AM   #3
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Quote:
Originally Posted by Bozza View Post
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.
Thanks from topsquark

Last edited by JeffM1; October 29th, 2017 at 11:04 AM.
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October 30th, 2017, 06:20 AM   #4
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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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