document.write( "Question 93986: The question is:\r
\n" ); document.write( "\n" ); document.write( "For all x > 0 and y > 0, the radical expression $\"+%28+sqrt%28x%29+%29+%2F+%28+3+%2A+sqrt%28x%29+-+sqrt%28y%29+%29+\"$ or \"[ sqrt(x) ] / [ (3) * sqrt(x) - sqrt(y) ]\" is equivalent to:\r
\n" ); document.write( "\n" ); document.write( "The answer is:\r
\n" ); document.write( "\n" ); document.write( " $\"%28+%28+3+%2A+x+%2B+sqrt%28xy%29+%29+%2F+%28+9x+-+y%29+%29\"$ \"[ 3x + sqrt(xy) ] / [9x - y]\"\r
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Algebra.Com's Answer #68435 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"+%28+sqrt%28x%29+%29+%2F+%28+3+%2A+sqrt%28x%29+-+sqrt%28y%29+%29+\"$ Start with the given expression\r
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Multiply the fraction by $\"%28+3+%2A+sqrt%28x%29+%2B+sqrt%28y%29+%29%2F%28+3+%2A+sqrt%28x%29+%2B+sqrt%28y%29+%29\"$ (which is a form of 1). This will rationalize the denominator.\r
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Combine the fractions\r
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Foil the denominator\r
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Multiply $\"%283+%2A+sqrt%28x%29%29%283+%2A+sqrt%28x%29%29\"$ to get $\"9x\"$ and multiply $\"-%28sqrt%28y%29%29%28sqrt%28y%29%29\"$ to get $\"-y\"$ \r
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Notice the common root terms in the denominator add and cancel to zero\r
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\n" ); document.write( "\n" ); document.write( " $\"%28+%28+sqrt%28x%29+%29%28+3+%2A+sqrt%28x%29+%2B+sqrt%28y%29+%29+%2F+%28+9x+-+y%29+%29\"$ Simplify\r
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Distribute $\"sqrt%28x%29\"$ in the numerator\r
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\n" ); document.write( "\n" ); document.write( " $\"%28+%28+3+%2A+x+%2B+sqrt%28xy%29+%29+%2F+%28+9x+-+y%29+%29\"$ Multiply and combine the root terms\r
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\n" ); document.write( "\n" ); document.write( "So $\"+%28+sqrt%28x%29+%29+%2F+%28+3+%2A+sqrt%28x%29+-+sqrt%28y%29+%29+\"$ is equivalent to $\"%28+%28+3+%2A+x+%2B+sqrt%28xy%29+%29+%2F+%28+9x+-+y%29+%29\"$ \n" ); document.write( "

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