document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=73191>Question 73191</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help, this is a complex fraction\r<BR>\n" );
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document.write( "12x + 16 + 5/x<BR>\n" );
document.write( "over<BR>\n" );
document.write( "18x - 27 - 35/x\r<BR>\n" );
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document.write( "Do I use x as a LCD, ?? 12x^2 + 16x + 5  over 18x^2 -27x -35  or would the x's cancel on the 12 and 18???????????? Please walk me through. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #52434 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=52434\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2812x+%2B+16+%2B+%285%2Fx%29%29%2F%2818x+-+27+-+%2835%2Fx%29%29 ALIGN=MIDDLE  ALT=\"%2812x+%2B+16+%2B+%285%2Fx%29%29%2F%2818x+-+27+-+%2835%2Fx%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You can use x as an LCD in both the numerator and denominator, but it may be quicker for<BR>\n" );
document.write( "you to just multiply the fraction (both numerator and denominator) by x. In effect this is<BR>\n" );
document.write( "multiplying the fraction of the problem by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Fx ALIGN=MIDDLE  ALT=\"x%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > which will not change the result of the<BR>\n" );
document.write( "division because it is the same as multiplying the fraction by 1.<BR>\n" );
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document.write( "Multiplying the numerator by x (all three terms are multiplied by x) results in changing<BR>\n" );
document.write( "the numerator to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12x%5E2+%2B+16x+%2B+5 ALIGN=MIDDLE  ALT=\"12x%5E2+%2B+16x+%2B+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Similarly, multiplying all three terms of the denominator by x changes the denominator<BR>\n" );
document.write( "to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18x%5E2+-+27x+-+35 ALIGN=MIDDLE  ALT=\"18x%5E2+-+27x+-+35\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "so the problem is now modified to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2812x%5E2+%2B+16x+%2B+5%29%2F%2818x%5E2+-+27x+-+35%29 ALIGN=MIDDLE  ALT=\"%2812x%5E2+%2B+16x+%2B+5%29%2F%2818x%5E2+-+27x+-+35%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The numerator factors to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%2B1%29%2A%286x%2B5%29 ALIGN=MIDDLE  ALT=\"%282x%2B1%29%2A%286x%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the denominator factors to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x-7%29%2A%286x%2B5%29 ALIGN=MIDDLE  ALT=\"%283x-7%29%2A%286x%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "so the problem becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%282x%2B1%29%2A%286x%2B5%29%29%2F%28%283x-7%29%2A%286x%2B5%29%29 ALIGN=MIDDLE  ALT=\"%28%282x%2B1%29%2A%286x%2B5%29%29%2F%28%283x-7%29%2A%286x%2B5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and canceling the common factor in the numerator and denominator:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%282x%2B1%29%2Across%286x%2B5%29%29%2F%28%283x-7%29%2Across%286x%2B5%29%29 ALIGN=MIDDLE  ALT=\"%28%282x%2B1%29%2Across%286x%2B5%29%29%2F%28%283x-7%29%2Across%286x%2B5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "reduces the problem to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%2B1%29%2F%283x-7%29 ALIGN=MIDDLE  ALT=\"%282x%2B1%29%2F%283x-7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and that is the answer.<BR>\n" );
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document.write( "Hope this provides a little easier way of looking at how to work the problem.  It is<BR>\n" );
document.write( "just a little more convenient than using the LCD, but the LCD method would work.<BR>\n" );
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