Can you solve this question?

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1 Answer
Mar 19, 2018

The answer is C) #-2x#

Explanation:

The first step is to multiply the top and bottom of each fraction by the denominator of the other fraction (sorry, this will be long!):

First Term:
#25/(x+sqrt(x^2+25))xx(-x+sqrt(x^2+25))/(-x+sqrt(x^2+25))#

#(25(-x+sqrt(x^2+25)))/((x+sqrt(x^2+25))(-x+sqrt(x^2+25)))#

#(25(-x+sqrt(x^2+25)))/(-x^2+(sqrt(x^2+25)^2)#

#(25(-x+sqrt(x^2+25)))/(cancel(-x^2+x^2)+25)#

#(cancel(25)(-x+sqrt(x^2+25)))/cancel(25)=color(red)(-x+sqrt(x^2+25))#

Second Term:
#-25/(-x+sqrt(x^2+25))xx(x+sqrt(x^2+25))/(x+sqrt(x^2+25))#

#-(25(x+sqrt(x^2+25)))/((-x+sqrt(x^2+25))(x+sqrt(x^2+25)))#

#-(25(x+sqrt(x^2+25)))/(-x^2+(sqrt(x^2+25)^2)#

#-(25(x+sqrt(x^2+25)))/(cancel(-x^2+x^2)+25)#

#-(cancel(25)(x+sqrt(x^2+25)))/cancel(25)=color(blue)(-(x+sqrt(x^2+25)))#

Put the first and second terms back together:

#color(red)(-x+sqrt(x^2+25))color(blue)(-(x+sqrt(x^2+25)))#

#color(red)(-x+cancel(sqrt(x^2+25)))color(blue)(-x-cancel(sqrt(x^2+25)))#

#color(red)(-x)color(blue)(-x)=color(green)(-2x)#