document.write( "Question 199880: Please show step by step. For all x>0 and y>0, the radical expression √x/3√x-√y is equivalent to \n" ); document.write( "

Algebra.Com's Answer #150242 by jim_thompson5910(35256) $\"\"$ $\"About$

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$\"%28sqrt%28x%29%29%2F%28sqrt%28x%29-sqrt%28y%29%29\"$ Start with the given expression.\r
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Multiply both the numerator and denominator by $\"sqrt%28x%29%2Bsqrt%28y%29\"$ \r
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FOIL\r
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\n" ); document.write( "\n" ); document.write( " $\"%28sqrt%28x%29%28sqrt%28x%29%2Bsqrt%28y%29%29%29%2F%28x-y%29\"$ Square the square roots.\r
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\n" ); document.write( "\n" ); document.write( " $\"%28sqrt%28x%29%2Asqrt%28x%29%2Bsqrt%28x%29%2Asqrt%28y%29%29%2F%28x-y%29\"$ Distribute\r
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\n" ); document.write( "\n" ); document.write( " $\"%28sqrt%28x%5E2%29%2Bsqrt%28xy%29%29%2F%28x-y%29\"$ Combine the roots.\r
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\n" ); document.write( "\n" ); document.write( " $\"%28x%2Bsqrt%28xy%29%29%2F%28x-y%29\"$ Take the square root of $\"x%5E2\"$ to get \"x\"\r
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\n" ); document.write( "\n" ); document.write( "So $\"%28sqrt%28x%29%29%2F%28sqrt%28x%29-sqrt%28y%29%29=%28x%2Bsqrt%28xy%29%29%2F%28x-y%29\"$ where $\"x%3E0\"$ , $\"y%3E0\"$ , and $\"x%3C%3Ey\"$ \r
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\n" ); document.write( "\n" ); document.write( "If you have any questions, email me at jim_thompson5910@hotmail.com.
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