document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=88232>Question 88232</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi there, \r<BR>\n" );
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document.write( "I have to express my answer in simplest form after adding this problem. The problem reads like this: 6/3x-2 + 3/2x. <BR>\n" );
document.write( "I'm not even really sure what to do, so any help you can give me would be greatly appreciated! \r<BR>\n" );
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document.write( "Thank you so much!! <BR>\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 #64113 by </B><A HREF=/tutors/aboutme.mpl?userid=longjonsilver><B>longjonsilver(2297)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=longjonsilver><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/cgi-bin/show-face.mpl?user=longjonsilver><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=64113\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> this is just a fraction problem. We treat it just like numerical fractions:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%286%2F%283x-2%29%29+%2B+%283%2F2x%29+ ALIGN=MIDDLE  ALT=\"+%286%2F%283x-2%29%29+%2B+%283%2F2x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "if we had <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%2F3+%2B+1%2F4+ ALIGN=MIDDLE  ALT=\"+2%2F3+%2B+1%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > we would have to find the LCM of both 3 and 4 --> 3*4 which we can evaluate --> 12.<BR>\n" );
document.write( "We do the same with (3x-2) and 2x. Their LCM is (3x-2)*2x which we cant evaluate so we leave it like that.\r<BR>\n" );
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document.write( "Next step is to multiply both fractions by 1 (so they remain unchanged) but write the 1 as a fraction:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%282%2F3%29%284%2F4%29+%2B+%281%2F4%29%283%2F3%29+ ALIGN=MIDDLE  ALT=\"+%282%2F3%29%284%2F4%29+%2B+%281%2F4%29%283%2F3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%288%2F12%29+%2B+%283%2F12%29+ ALIGN=MIDDLE  ALT=\"+%288%2F12%29+%2B+%283%2F12%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%2811%2F12%29+ ALIGN=MIDDLE  ALT=\"+%2811%2F12%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Algebraically we cannot do all these steps. We can do the first one:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%286%2F%283x-2%29%29%2A%28%282x%29%2F%282x%29%29+%2B+%283%2F2x%29%2A%28%283x-2%29%2F%283x-2%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We can multiply the numerators together and the denominators too:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%286%282x%29%29%2F%28%282x%29%283x-2%29%29+%2B+%283%283x-2%29%29%2F%282x%283x-2%29%29+ ALIGN=MIDDLE  ALT=\"+%286%282x%29%29%2F%28%282x%29%283x-2%29%29+%2B+%283%283x-2%29%29%2F%282x%283x-2%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "And now add them together since they have the same denominator:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%286%282x%29+%2B+3%283x-2%29%29%2F%28%282x%29%283x-2%29%29+ ALIGN=MIDDLE  ALT=\"+%286%282x%29+%2B+3%283x-2%29%29%2F%28%282x%29%283x-2%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So that is the fractions done. The rest is just manipulation of the algebra to try to simplify it:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%2812x+%2B+3%283x-2%29%29%2F%28%282x%29%283x-2%29%29+ ALIGN=MIDDLE  ALT=\"+%2812x+%2B+3%283x-2%29%29%2F%28%282x%29%283x-2%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%2812x+%2B+9x-6%29%2F%28%282x%29%283x-2%29%29+ ALIGN=MIDDLE  ALT=\"+%2812x+%2B+9x-6%29%2F%28%282x%29%283x-2%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%2821x-6%29%2F%28%282x%29%283x-2%29%29+ ALIGN=MIDDLE  ALT=\"+%2821x-6%29%2F%28%282x%29%283x-2%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "or perhaps multiply out the denominator:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%2821x-6%29%2F%286x%5E2-4x%29+ ALIGN=MIDDLE  ALT=\"+%2821x-6%29%2F%286x%5E2-4x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "but we tend not to do this - we like things factorised. The answer is best quoted as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%2821x-6%29%2F%28%282x%29%283x-2%29%29+ ALIGN=MIDDLE  ALT=\"+%2821x-6%29%2F%28%282x%29%283x-2%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "hope this helps\r<BR>\n" );
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document.write( "cheers<BR>\n" );
document.write( "Jon.<BR>\n" );
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