SOLUTION: Rationalize the numerator. Assume that all variables represent positive real numbers. {{{ sqrt( x+5 ) }}} - {{{sqrt( x ) }}} ___________ ___________ __________ 5

Algebra ->  Radicals -> SOLUTION: Rationalize the numerator. Assume that all variables represent positive real numbers. {{{ sqrt( x+5 ) }}} - {{{sqrt( x ) }}} ___________ ___________ __________ 5       Log On


   

Question 1107968: Rationalize the numerator. Assume that all variables represent positive real numbers.
+sqrt%28+x%2B5+%29+ - sqrt%28+x+%29+
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5
the "__" means that it is a fraction, 5 is the denominator!
thank you
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Rationalize the numerator. Assume that all variables represent positive real numbers.
[sqrt( x+5 ) - sqrt( x )]/5
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Multiply numerator and denominator by sqrt(x+5)+sqrt(x) to get:
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(sqrt(x+5))^2 - (sqrt(x))^2]/[5sqrt(x+5)+5sqrt(x)]
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= [x+5-x]/[5sqrt(x+5)+5sqrt(x)]
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= 5/[5sqrt(x+5)+5sqrt(x)]
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Cheers,
Stan H.
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