How do you solve #sqrt(x+3)-sqrt(x-1)=1#?

1 Answer
Alan P.
Aug 31, 2016

#color(green)(x=13/4 = 3 1/4)#

Explanation:

Given
#color(white)("XXX")sqrt(x+3)-sqrt(x-1)=1#

#color(white)("XXX")rarr sqrt(x+3)=1+sqrt(x-1)#

Squaring both sides:
#color(white)("XXX")cancel(x)+3=cancel(1)+2sqrt(x-1)+cancel(x)cancel(-1)#

#color(white)("XXX")rarr 2sqrt(x-1)=3#

#color(white)("XXX")rarr sqrt(x-1)=3/2#

Squaring both sides again
#color(white)("XXX")rarr x-1=9/4#

#color(white)("XXX")rarr x=13/4#

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