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December 24th, 2017, 03:51 PM  #1 
Newbie Joined: Jan 2014 Posts: 19 Thanks: 0  Equality of two expressions
Are the following two expressions equal? $\displaystyle (4(x^52))/$$\displaystyle ((8+x^5)^2\sqrt{\frac{x}{5x^5+40}})$ $\displaystyle (4\sqrt{5}(2x^5))/$$\displaystyle \sqrt{x(8+x^5)^3}$ 
December 24th, 2017, 04:36 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 19,974 Thanks: 1850 
For real values of x such that no denominator is zero, yes.

December 24th, 2017, 09:17 PM  #3  
Senior Member Joined: May 2016 From: USA Posts: 1,206 Thanks: 494  Quote:
$\dfrac{\ 4(x^5  2)}{(8 + x^5)^2 * \sqrt{\dfrac{x}{5x^5 + 40}}} = \dfrac{4(2  x^5)}{(8 + x^5)^2 * \sqrt{\dfrac{x}{5x^5 + 40}}} = \dfrac{4(2  x^5)}{ \sqrt{(8 + x^5 )^4} * \sqrt{\dfrac{x}{5x^5 + 40}}} =$ $ \dfrac{4(2  x^5)}{\sqrt{(8 + x^5)^4} * \sqrt{\dfrac{x}{5(8 + x^5)}}} = \dfrac{4(2  x^5)}{\sqrt{\dfrac{x(8 + x^5)^4}{5(8 + x^5)}}} = \dfrac{4(2  x^5)}{\sqrt{\dfrac{x(8 + x^5)^3}{5}}} =$ $ \dfrac{4(2  x^5)}{\dfrac{\sqrt{x(8 + x^5)^3}}{\sqrt{5}}} = \dfrac{4 \sqrt{5} * (2  x^5)}{\sqrt{x(8 + x^5)^3}}.$  

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