document.write( "Question 514219: Rationalize 2A/B1/3 \n" ); document.write( "
Algebra.Com's Answer #343325 by xdragonfight(116)\"\" \"About 
You can put this solution on YOUR website!
a) (1/√2)/(1 − (1/√2)) * (1 + (1/√2))/(1 + (1/√2))
\n" ); document.write( "= [(1/√2) * (1 + (1/√2))] / (1 - 1/2)
\n" ); document.write( "= [(1/√2) + 1/2] / (1/2)
\n" ); document.write( "= 1 + (2/√2)
\n" ); document.write( "= (√2 + 2)/√2 * √2/√2
\n" ); document.write( "= 1 + √2\r
\n" ); document.write( "\n" ); document.write( "Edit: a) can be simplified first:
\n" ); document.write( "a) (1/√2)/(1 − (1/√2))
\n" ); document.write( "= 1/(√2 - 1) * (√2 + 1)/(√2 + 1)
\n" ); document.write( "= (√2 +1)/(2 - 1)
\n" ); document.write( "= 1 + √2\r
\n" ); document.write( "\n" ); document.write( "Also b) can be simplified:
\n" ); document.write( "b) (1 + (1/√2))/(1 − (1/√2))
\n" ); document.write( "= (√2 + 1)/ √2 / (√2 - 1) / √2
\n" ); document.write( "= (√2 + 1) / (√2 - 1) * (√2 + 1) / (√2 + 1)
\n" ); document.write( "= (√2 + 1)^2 / (2 - 1)
\n" ); document.write( "= 3 + 2√2
\n" ); document.write( "
\n" );