document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=220109>Question 220109</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how do you solve \r<BR>\n" );
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document.write( "(6x^(-1/3)+2x^5/3)/2x^-4/3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #165326 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=165326\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286x%5E%28-1%2F3%29%2B2x%5E%285%2F3%29%29%2F%282x%5E%28-4%2F3%29%29 ALIGN=MIDDLE  ALT=\"%286x%5E%28-1%2F3%29%2B2x%5E%285%2F3%29%29%2F%282x%5E%28-4%2F3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "First let's reduce the fraction. Reduced fractions are usually easier to work with. Since 2 is a common factor we can reduce the fraction be a factor of 2:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286x%5E%28-1%2F3%29%2B2x%5E%285%2F3%29%29%2F%282x%5E%28-4%2F3%29%29+=+%282%283x%5E%28-1%2F3%29%2Bx%5E%285%2F3%29%29%29%2F%282x%5E%28-4%2F3%29%29+=+%283x%5E%28-1%2F3%29%2Bx%5E%285%2F3%29%29%2F%28x%5E%28-4%2F3%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "From this point there are, as usual, a number of ways we can go. The most direct way to the answer is to multiply the numerator and denominator by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E%284%2F3%29 ALIGN=MIDDLE  ALT=\"x%5E%284%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. (I hope you can see that this will turn the denominator into a 1 which, in turn, means that we will no longer have a fraction. And not having a fraction anymore is, I hope you agree, a good thing.):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x%5E%28-1%2F3%29%2Bx%5E%285%2F3%29%29%2F%28x%5E%28-4%2F3%29%29+=+%28%283x%5E%28-1%2F3%29%2Bx%5E%285%2F3%29%29%2F%28x%5E%28-4%2F3%29%29%29%28%28x%5E%284%2F3%29%29%2F%28x%5E%284%2F3%29%29%29+=%0D%0A%28%283x%5E%28-1%2F3%29%2Bx%5E%285%2F3%29%29%28x%5E%284%2F3%29%29%29%2F%28x%5E%28-4%2F3%29%2Ax%5E%284%2F3%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "In the denominator, since<ul><li>the rule for exponents when you multiply is to add the exponents, and</li><li>-4/3 + 4/3 = 0, and</li><li><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E0+=+1 ALIGN=MIDDLE  ALT=\"x%5E0+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ></li></ul>the denominator becomes a 1!<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%283x%5E%28-1%2F3%29%2Bx%5E%285%2F3%29%29%28x%5E%284%2F3%29%29%29%2F%28x%5E%28-4%2F3%29%2Ax%5E%284%2F3%29%29+=+++++++++++++++++++++++++++++++++%28%283x%5E%28-1%2F3%29%2Bx%5E%285%2F3%29%29%28x%5E%284%2F3%29%29%29%2F1+=+%283x%5E%28-1%2F3%29%2Bx%5E%285%2F3%29%29%28x%5E%284%2F3%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now let's simplify using the Distributive Property:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x%5E%28-1%2F3%29%2Bx%5E%285%2F3%29%29%28x%5E%284%2F3%29%29+=+3x%5E%28-1%2F3%29%2Ax%5E%284%2F3%29%2Bx%5E%285%2F3%29x%5E%284%2F3%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Again we'll use the \"add the exponents when multiplying\" rule:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E%28-1%2F3%29%2Ax%5E%284%2F3%29%2Bx%5E%285%2F3%29x%5E%284%2F3%29+=+3x%5E%283%2F3%29%2Bx%5E%289%2F3%29+=+3x%5E1+%2B+x%5E3+=+3x+%2B+x%5E3 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "And we're finished! </SPAN>\n" );
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