document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=93381>Question 93381</A>: <I><SPAN STYLE=\"word-break: break-all;\"> been researching this problem and i believe it is an inconsistent equation<BR>\n" );
document.write( "after I have factored all the denominators and try to multiply through to get rid of the fractions and continue working the problem get stuck.All the other problems I have done before have the same combinations once factored not the case here.\r<BR>\n" );
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document.write( "4/(x^2+3x-10)-1/(x^2+x-6)=3/(x^2-x-12) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #68104 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=68104\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> From your answer I gathered that you understand the methods that need to be applied to solve<BR>\n" );
document.write( "the problem, but you are probably making a minor math mistake somewhere that is leading you astray.<BR>\n" );
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document.write( "There is a solution for x and here's how you go about getting it. <BR>\n" );
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document.write( "Start with the given problem:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F%28x%5E2%2B3x-10%29+-+1%2F%28x%5E2%2Bx-6%29+=+3%2F%28x%5E2-x-12%29 ALIGN=MIDDLE  ALT=\"4%2F%28x%5E2%2B3x-10%29+-+1%2F%28x%5E2%2Bx-6%29+=+3%2F%28x%5E2-x-12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Factor each of the three denominators. When you do you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F%28%28x%2B5%29%28x-2%29%29+-+1%2F%28%28x%2B3%29%28x-2%29%29+=+3%2F%28%28x-4%29%28x%2B3%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Then identify each of the individual factors. The list is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-2 ALIGN=MIDDLE  ALT=\"x-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B5 ALIGN=MIDDLE  ALT=\"x%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3 ALIGN=MIDDLE  ALT=\"x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-4 ALIGN=MIDDLE  ALT=\"x-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "When you multiply these together, you get a common denominator that can be used for each<BR>\n" );
document.write( "term.  As an abbreviation, use CD for this common denominator.<BR>\n" );
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document.write( "To put a term over this common denominator, you must multiply its numerator by those factors<BR>\n" );
document.write( "in the common denominator that were not in its original denominator. Putting the terms over <BR>\n" );
document.write( "the common denominator results in:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%28x%2B3%29%28x-4%29%29%2F%28CD%29+-+%28%28x%2B5%29%28x-4%29%29%2F%28CD%29+=+%283%28x-2%29%28x%2B5%29%29%2F%28CD%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now you can get rid of the CD by multiplying both sides of this equation (all terms) by <BR>\n" );
document.write( "the CD. When you do that the CD multiplier cancels with the CD in the denominator<BR>\n" );
document.write( "and you are left with just the numerators of the terms in the problem.  That is, you are<BR>\n" );
document.write( "left with:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28x%2B3%29%28x-4%29+-+%28x%2B5%29%28x-4%29+=+3%28x-2%29%28x%2B5%29 ALIGN=MIDDLE  ALT=\"4%28x%2B3%29%28x-4%29+-+%28x%2B5%29%28x-4%29+=+3%28x-2%29%28x%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "In each of the three groupings, multiply the two sets of parentheses to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28x%5E2+-x+-12%29-+%28x%5E2%2Bx-20%29=+3%28x%5E2%2B3x-10%29 ALIGN=MIDDLE  ALT=\"4%28x%5E2+-x+-12%29-+%28x%5E2%2Bx-20%29=+3%28x%5E2%2B3x-10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now multiply by the constants in front of the parentheses (note that in the second term<BR>\n" );
document.write( "on the left side the constant is -1). When you do those multiplications you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2+-4x+-48+-x%5E2+-+x+%2B20+=+3x%5E2+%2B9x+-30 ALIGN=MIDDLE  ALT=\"4x%5E2+-4x+-48+-x%5E2+-+x+%2B20+=+3x%5E2+%2B9x+-30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Combine the like terms on each side of the equation. On the left side you have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2 ALIGN=MIDDLE  ALT=\"4x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%5E2 ALIGN=MIDDLE  ALT=\"-x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > which combine to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2 ALIGN=MIDDLE  ALT=\"3x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. You also have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4x ALIGN=MIDDLE  ALT=\"-4x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x ALIGN=MIDDLE  ALT=\"-x\"   DISABLED_style= \"max-width:90%; height:auto;\" > which combine<BR>\n" );
document.write( "to -5x. And finally you have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-48 ALIGN=MIDDLE  ALT=\"-48\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20 ALIGN=MIDDLE  ALT=\"20\"   DISABLED_style= \"max-width:90%; height:auto;\" > which combine to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-28 ALIGN=MIDDLE  ALT=\"-28\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "So the left<BR>\n" );
document.write( "side is reduced to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2-5x-28 ALIGN=MIDDLE  ALT=\"3x%5E2-5x-28\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2+-5x-28+=+3x%5E2+%2B+9x+-+30 ALIGN=MIDDLE  ALT=\"3x%5E2+-5x-28+=+3x%5E2+%2B+9x+-+30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "If you subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2 ALIGN=MIDDLE  ALT=\"3x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides, the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2 ALIGN=MIDDLE  ALT=\"3x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > terms on the left and the right<BR>\n" );
document.write( "side are eliminated and you are left with:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5x-28+=+9x-30 ALIGN=MIDDLE  ALT=\"-5x-28+=+9x-30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Subtract 9x from both sides and the equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-14x-28+=+-30 ALIGN=MIDDLE  ALT=\"-14x-28+=+-30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Add +28 to both sides and you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-14x+=+-2 ALIGN=MIDDLE  ALT=\"-14x+=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Finally solve for x by dividing both sides by -14 and you have:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-2%29%2F%28-14%29+=+1%2F7 ALIGN=MIDDLE  ALT=\"x+=+%28-2%29%2F%28-14%29+=+1%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "And that's the answer ... <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+1%2F7 ALIGN=MIDDLE  ALT=\"x+=+1%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Hope this helps you to find your math error.<BR>\n" );
document.write( " </SPAN>\n" );
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