document.write( "Question 274592: Rationalize the denominator assume all expressions under radicals represent positive numbers.\r
\n" ); document.write( "\n" ); document.write( "(2-√y)/(3+√y) please help, I have trouble with these\r
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Algebra.Com's Answer #200366 by dabanfield(803)\"\" \"About 
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(2-√y)/(3+√y)\r
\n" ); document.write( "\n" ); document.write( "To eliminate a radical in the denominator we can multiply both the numerator and denominator by the \"conjugate\" of the denominator. This is the same a multiplying by 1 so the value of the expression is not changed by doing this. In this case the conjugate of 3+sqrt(y) is 3-sqrt(y) so we have:\r
\n" ); document.write( "\n" ); document.write( "[(2-sqrt(y)*(3-sqrt(y)]/[(3+sqrt(y)*(3-sqrt(y))]\r
\n" ); document.write( "\n" ); document.write( "Using FOIL above the numerator becomes:\r
\n" ); document.write( "\n" ); document.write( "2*3 - 2*sqrt(y) - 3*sqrt(y) + sqrt(y)*sqrt(y) =\r
\n" ); document.write( "\n" ); document.write( "6 - 5*sqrt(y) + sqrt(y*y) =\r
\n" ); document.write( "\n" ); document.write( "6 - 5*sqrt(y) + y\r
\n" ); document.write( "\n" ); document.write( "The denominator becomes:\r
\n" ); document.write( "\n" ); document.write( "3*3 - 3 sqrt(y) + 3*sqrt(y) - sqrt(y)*sqrt(y) =\r
\n" ); document.write( "\n" ); document.write( "9 - sqrt(y*y) =\r
\n" ); document.write( "\n" ); document.write( "9 - y\r
\n" ); document.write( "\n" ); document.write( "Putting numerator and denominator together then we have:\r
\n" ); document.write( "\n" ); document.write( "(6 - 5*sqrt(y) + y)/(9 - y)\r
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