document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=24272>Question 24272</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Simplify\r<BR>\n" );
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document.write( "(2x^3 /(sqaure root of x^3 + 4)) + (5(square root of x^3 + 4))\r<BR>\n" );
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document.write( "I just don't know what to do with the square roots when trying to simply<BR>\n" );
document.write( "Thanks<BR>\n" );
document.write( "Tiffany<BR>\n" );
document.write( "P.S. Sorry I didn't know how to type a sqaure root sign so I just wrote it  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #12903 by </B><A HREF=/tutors/aboutme.mpl?userid=kev82><B>kev82(151)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=kev82><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=12903\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi,\r<BR>\n" );
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document.write( "This is actually a really easy fractions problem, hidden behind some horrible looking algebra. All you have to do is remember how to add fractions. Let's try a simple example:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F5+%2B+2%2F7 ALIGN=MIDDLE  ALT=\"1%2F5+%2B+2%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We need to work out a common denominator for ecah of the fractions. A common denomitator, is just a common multiple of 5 and 7. The most obvious choice is 35. Now we rewite the fractions:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F5=7%2F35 ALIGN=MIDDLE  ALT=\"1%2F5=7%2F35\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F7=10%2F35 ALIGN=MIDDLE  ALT=\"2%2F7=10%2F35\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now we add them giving <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287%2B10%29%2F35=17%2F35 ALIGN=MIDDLE  ALT=\"%287%2B10%29%2F35=17%2F35\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Doing the same thing with your problem we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%5E3%29%2Fsqrt%28x%5E3%2B4%29%2B5%2Asqrt%28x%5E3%2B4%29%2F1 ALIGN=MIDDLE  ALT=\"%282x%5E3%29%2Fsqrt%28x%5E3%2B4%29%2B5%2Asqrt%28x%5E3%2B4%29%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Taking <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%5E3%2B4%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%5E3%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as the common denominator, we rewrite the problem as\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%5E3%29%2Fsqrt%28x%5E3%2B4%29%2B5%2Asqrt%28x%5E3%2B4%29%2Asqrt%28x%5E3%2B4%29%2Fsqrt%28x%5E3%2B4%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "But notice that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%5E3%2B4%29%2Asqrt%28x%5E3%2B4%29=sqrt%28x%5E3%2B4%29%5E2 ALIGN=MIDDLE  ALT=\"sqrt%28x%5E3%2B4%29%2Asqrt%28x%5E3%2B4%29=sqrt%28x%5E3%2B4%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is just <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3%2B4 ALIGN=MIDDLE  ALT=\"x%5E3%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Using this, and adding the fractions, we get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2Ax%5E3%2B5%2A%28x%5E3%2B4%29%29%2Fsqrt%28x%5E3%2B4%29 ALIGN=MIDDLE  ALT=\"%282%2Ax%5E3%2B5%2A%28x%5E3%2B4%29%29%2Fsqrt%28x%5E3%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "I'm sure you can tidy that up to get an answer of\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287x%5E3%2B20%29%2Fsqrt%28x%5E3%2B4%29 ALIGN=MIDDLE  ALT=\"%287x%5E3%2B20%29%2Fsqrt%28x%5E3%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "At university level you would be expected to either show the fraction is in it's lowest form, or cancel it to it's lowest form. But factoring cubics is probably too hard for schoolwork, so I'll just tell you that this is as simplified as it gets.\r<BR>\n" );
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document.write( "Hope that helps\r<BR>\n" );
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document.write( "Kev </SPAN>\n" );
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