document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1192822>Question 1192822</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Rationalize the denominator\r<BR>\n" );
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document.write( "sqrt(2x)/sqrt(x)-sqrt(10) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #824736 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=824736\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%282x%29%29%2F%28sqrt%28x%29-sqrt%2810%29%29 ALIGN=MIDDLE  ALT=\"%28sqrt%282x%29%29%2F%28sqrt%28x%29-sqrt%2810%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is in the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%2F%28B-C%29 ALIGN=MIDDLE  ALT=\"A%2F%28B-C%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+sqrt%282x%29 ALIGN=MIDDLE  ALT=\"A+=+sqrt%282x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B+=+sqrt%28x%29 ALIGN=MIDDLE  ALT=\"B+=+sqrt%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+=+sqrt%2810%29 ALIGN=MIDDLE  ALT=\"C+=+sqrt%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Multiply top and bottom by (B+C)<BR>\n" );
document.write( "This way we have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28B-C%29%28B%2BC%29+=+B%5E2+-+C%5E2+=+%28sqrt%28x%29%29%5E2+-+%28sqrt%2810%29%29%5E2+=+x+-+10 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > in the denominator, thereby rationalizing it (i.e. removing the square root terms from the denominator). Refer to the difference of squares rule.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%2F%28B-C%29 ALIGN=MIDDLE  ALT=\"A%2F%28B-C%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28A%28B%2BC%29%29%2F%28B%5E2+-+C%5E2%29 ALIGN=MIDDLE  ALT=\"%28A%28B%2BC%29%29%2F%28B%5E2+-+C%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%282x%29%2A%28sqrt%28x%29%2Bsqrt%2810%29%29%29%2F%28x-10%29 ALIGN=MIDDLE  ALT=\"%28sqrt%282x%29%2A%28sqrt%28x%29%2Bsqrt%2810%29%29%29%2F%28x-10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%282x%29%2Asqrt%28x%29%2Bsqrt%282x%29%2Asqrt%2810%29%29%2F%28x-10%29 ALIGN=MIDDLE  ALT=\"%28sqrt%282x%29%2Asqrt%28x%29%2Bsqrt%282x%29%2Asqrt%2810%29%29%2F%28x-10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%282x%2Ax%29%2Bsqrt%282x%2A10%29%29%2F%28x-10%29 ALIGN=MIDDLE  ALT=\"%28sqrt%282x%2Ax%29%2Bsqrt%282x%2A10%29%29%2F%28x-10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%282x%5E2%29%2Bsqrt%2820x%29%29%2F%28x-10%29 ALIGN=MIDDLE  ALT=\"%28sqrt%282x%5E2%29%2Bsqrt%2820x%29%29%2F%28x-10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%28x%5E2%2A2%29%2Bsqrt%284%2A5x%29%29%2F%28x-10%29 ALIGN=MIDDLE  ALT=\"%28sqrt%28x%5E2%2A2%29%2Bsqrt%284%2A5x%29%29%2F%28x-10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%28x%5E2%29%2Asqrt%282%29%2Bsqrt%284%29%2Asqrt%285x%29%29%2F%28x-10%29 ALIGN=MIDDLE  ALT=\"%28sqrt%28x%5E2%29%2Asqrt%282%29%2Bsqrt%284%29%2Asqrt%285x%29%29%2F%28x-10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2Asqrt%282%29%2B2%2Asqrt%285x%29%29%2F%28x-10%29 ALIGN=MIDDLE  ALT=\"%28x%2Asqrt%282%29%2B2%2Asqrt%285x%29%29%2F%28x-10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Therefore,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%282x%29%29%2F%28sqrt%28x%29-sqrt%2810%29%29+=+%28x%2Asqrt%282%29%2B2%2Asqrt%285x%29%29%2F%28x-10%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "such that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%3E=+0 ALIGN=MIDDLE  ALT=\"x+%3E=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%3C%3E+10 ALIGN=MIDDLE  ALT=\"x+%3C%3E+10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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