document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=148121>Question 148121</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Combine \r<BR>\n" );
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document.write( "4         \r\n" );
document.write( "---       -   x^(1/3)\r\n" );
document.write( "x^(2/3)\r\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #108508 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=108508\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{4}{x^{\frac{2}{3}}}-x^{\frac{1}{3}}\"> Start with the given expression.\r<BR>\n" );
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document.write( "Notice how the LCD is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x^{\frac{2}{3}}\">. So we need to multiply the second term <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x^{\frac{1}{3}}\"> by the LCD <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x^{\frac{2}{3}}\">. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{4}{x^{\frac{2}{3}}}-\left(x^{\frac{1}{3}}\right)\left(\frac{x^{\frac{2}{3}}}{x^{\frac{2}{3}}}\right)\"> Multiply the second term by the LCD\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{4}{x^{\frac{2}{3}}}-\left(\frac{x^{\frac{1}{3}}x^{\frac{2}{3}}}{x^{\frac{2}{3}}}\right)\"> Combine the fractions.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{4}{x^{\frac{2}{3}}}-\left(\frac{x^{\frac{1}{3}+\frac{2}{3}}}{x^{\frac{2}{3}}}\right)\"> Multiply the terms by adding the exponents.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{4}{x^{\frac{2}{3}}}-\left(\frac{x^{\frac{3}{3}}}{x^{\frac{2}{3}}}\right)\"> Add.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{4}{x^{\frac{2}{3}}}-\left(\frac{x^{1}}{x^{\frac{2}{3}}}\right)\"> Reduce.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{4}{x^{\frac{2}{3}}}-\left(\frac{x}{x^{\frac{2}{3}}}\right)\"> Simplify.\r<BR>\n" );
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document.write( "Since the denominators are now the same, we can add the fractions.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{4-x}{x^{\frac{2}{3}}}\"> Combine the numerators over the common denominator.\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{4}{x^{\frac{2}{3}}}-x^{\frac{1}{3}}\"> simplifies to <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{4-x}{x^{\frac{2}{3}}}\">\r<BR>\n" );
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document.write( "In other words, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{4}{x^{\frac{2}{3}}}-x^{\frac{1}{3}}=\frac{4-x}{x^{\frac{2}{3}}}\"> where x is positive and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C%3E0 ALIGN=MIDDLE  ALT=\"x%3C%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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