document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=252914>Question 252914</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I'm trying to rationalize the denominator of this of this equation <BR>\n" );
document.write( " x^2+x/sqrt(5x)+x \r<BR>\n" );
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document.write( "Thank you and happy new year!!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #185039 by </B><A HREF=/tutors/aboutme.mpl?userid=drk><B>drk(1908)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drk><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=185039\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The equation i think is this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2Bx%29%2F%28sqrt%285x%29%2Bx%29 ALIGN=MIDDLE  ALT=\"%28x%5E2%2Bx%29%2F%28sqrt%285x%29%2Bx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "step 1: to rationalize we multiply by a conjugate: sqrt(5x) - x in both numerator and denominator as:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2Bx%29%2F%28sqrt%285x%29%2Bx%29 ALIGN=MIDDLE  ALT=\"%28x%5E2%2Bx%29%2F%28sqrt%285x%29%2Bx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > * <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%285x%29-x%29+%2F+%28sqrt%285x%29+-+x%29 ALIGN=MIDDLE  ALT=\"%28sqrt%285x%29-x%29+%2F+%28sqrt%285x%29+-+x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "By foil we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X%5E2%2Asqrt%285x%29+-+x%5E3+%2B+x%2Asqrt%285x%29+-+x%5E2 ALIGN=MIDDLE  ALT=\"X%5E2%2Asqrt%285x%29+-+x%5E3+%2B+x%2Asqrt%285x%29+-+x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > / <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x+-+x%5E2 ALIGN=MIDDLE  ALT=\"5x+-+x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now, notice we can factor our, or cancel an x from everything. So, we get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X%2Asqrt%285x%29+-+x%5E2+%2B+sqrt%285x%29+-+x ALIGN=MIDDLE  ALT=\"X%2Asqrt%285x%29+-+x%5E2+%2B+sqrt%285x%29+-+x\"   DISABLED_style= \"max-width:90%; height:auto;\" > / <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5+-+x ALIGN=MIDDLE  ALT=\"5+-+x\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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