SOLUTION: The question is: For all x > 0 and y > 0, the radical expression {{{ ( sqrt(x) ) / ( 3 * sqrt(x) - sqrt(y) ) }}} or "[ sqrt(x) ] / [ (3) * sqrt(x)

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Question 93986: The question is:
For all x > 0 and y > 0, the radical expression or "[ sqrt(x) ] / [ (3) * sqrt(x) - sqrt(y) ]" is equivalent to:
The answer is:
"[ 3x + sqrt(xy) ] / [9x - y]"
How did they get this answer?
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
Start with the given expression

Multiply the fraction by (which is a form of 1). This will rationalize the denominator.

Combine the fractions

Foil the denominator

Multiply to get and multiply to get

Notice the common root terms in the denominator add and cancel to zero

Simplify

Distribute in the numerator

Multiply and combine the root terms

So is equivalent to

SOLUTION: The question is: For all x > 0 and y > 0, the radical expression {{{ ( sqrt(x) ) / ( 3 * sqrt(x) - sqrt(y) ) }}} or "[ sqrt(x) ] / [ (3) * sqrt(x) - sqrt(y) ]" is equivalent t