document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=165066>Question 165066</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine the total area of the trapezoid shown below. Express your answer as a rational expression (single fraction) in factored form.\r<BR>\n" );
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document.write( "Using the formula 1/2(x1 + X2) X h\r<BR>\n" );
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document.write( "When:\r<BR>\n" );
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document.write( "x1 = (x-2) / (1 + x)<BR>\n" );
document.write( "x2 = (12x - 3) / (2x^2 - x - 3)<BR>\n" );
document.write( "h = 27 - 8x^3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #121729 by </B><A HREF=/tutors/aboutme.mpl?userid=MRperkins><B>MRperkins(300)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MRperkins><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=MRperkins><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=121729\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the answer I get is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x-2%29%28x-3%29%28x%2B2%29%283-2x%29%28x%5E2%2B3x%2B9%29%2B3%284x-1%29%281%2Bx%29%283-2x%29%28x%5E2%2B3x%2B9%29%29%2F%282%281%2Bx%29%28x-3%29%28x%2B2%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Email me and I will send you a .pdf file with the work.<BR>\n" );
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document.write( "justin.sheppard.tech@hotmail.com\r<BR>\n" );
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document.write( "As a tutor, I only see the question.  I do not see who posted the question.  It is easiest for me to work the problem out on a piece of paper, scan the paper, and email it to the student.  There is a lot less typing and looking at a computer screen.\r<BR>\n" );
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document.write( "Here is my work:<BR>\n" );
document.write( "Given <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%28x1%2Bx2%29h ALIGN=MIDDLE  ALT=\"%281%2F2%29%28x1%2Bx2%29h\"   DISABLED_style= \"max-width:90%; height:auto;\" > area of a trapezoid<BR>\n" );
document.write( "where <BR>\n" );
document.write( "x1=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29%2F%281%2Bx%29 ALIGN=MIDDLE  ALT=\"%28x-2%29%2F%281%2Bx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x2=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2812x-3%29%2F%282x%5E2-x-3%29 ALIGN=MIDDLE  ALT=\"%2812x-3%29%2F%282x%5E2-x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "h=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=27-8%5E3 ALIGN=MIDDLE  ALT=\"27-8%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%28%28x-2%29%2F%281%2Bx%29%2B%2812x-3%29%2F%282x%5E2-x-3%29%29%2827-8x%5E3%29 ALIGN=MIDDLE  ALT=\"%281%2F2%29%28%28x-2%29%2F%281%2Bx%29%2B%2812x-3%29%2F%282x%5E2-x-3%29%29%2827-8x%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Factor everything to it's simplest form and you get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%28%28x-2%29%2F%281%2Bx%29%2B%283%284x-1%29%29%2F%28x-3%28x%2B2%29%29%29%283-2x%29%289%2B3x%2Bx%5E2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Note: Use the rule for factoring the difference of two perfect cubes when factoring (27-8x^3) which is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5E3-B%5E3=%28A-B%29%28A%5E2%2BAB%2BB%29 ALIGN=MIDDLE  ALT=\"A%5E3-B%5E3=%28A-B%29%28A%5E2%2BAB%2BB%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ". <BR>\n" );
document.write( "In order to add two expressions you need to have the same denominator (you must have the same thing on the bottom of the fraction) <BR>\n" );
document.write( "You must find the LCM which in this case is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2Bx%29%28x-3%29%28x%2B2%29 ALIGN=MIDDLE  ALT=\"%281%2Bx%29%28x-3%29%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "any number divided by the same number equals 1 <BR>\n" );
document.write( "any number times 1=itself<BR>\n" );
document.write( "therefore you can multiply the numerator and denominator in this problem by whatever is missing to make the denominator = to the LCM. <BR>\n" );
document.write( "In this case the LEFT expression is missing <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%28x%2B2%29 ALIGN=MIDDLE  ALT=\"%28x-3%29%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > so you would multiply the expression by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x-3%29%28x%2B2%29%2F%28x-3%29%28x%2B2%29%29 ALIGN=MIDDLE  ALT=\"%28%28x-3%29%28x%2B2%29%2F%28x-3%29%28x%2B2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "In this case the RIGHT expression is missing <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2Bx%29 ALIGN=MIDDLE  ALT=\"%281%2Bx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > so you would multiply the expression by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%2B1%29%2F%28x%2B1%29%29 ALIGN=MIDDLE  ALT=\"%28%28x%2B1%29%2F%28x%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "so we get<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%28%28x-2%29%28x-3%29%28x%2B2%29%2F%281%2Bx%29%28x-3%29%28x%2B2%29%2B%283%284x-1%29%281%2Bx%29%29%2F%28x-3%29%28x%2B2%29%281%2Bx%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%283-2x%29%289%2B3x%2B3x%5E2%29%29 ALIGN=MIDDLE  ALT=\"%28%283-2x%29%289%2B3x%2B3x%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".Multiply through and you get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x-2%29%28x-3%29%28x%2B2%29%283-2x%29%289%2B3x%2B3x%5E2%29%2B3%284x-1%29%281%2Bx%29%283-2x%29%289%2B3x%2B3x%5E2%29%29%2F2%28x-3%29%28x%2B2%29%281%2Bx%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ". <BR>\n" );
document.write( "In true factored form I guess it would be written:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28%283-2x%29%289%2B3x%2B3x%5E2%29%29%28%28x-2%29%28x-3%29%28x%2B2%29%2B3%284x-1%29%281%2Bx%29%29%29%2F%282%28x-3%29%28x%2B2%29%281%2Bx%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Tutoring available<BR>\n" );
document.write( "Contact justin.sheppard.tech@hotmail.com for details </SPAN>\n" );
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