document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203631>Question 1203631</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find A, B and C if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%2F%28x-1%29 ALIGN=MIDDLE  ALT=\"A%2F%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B%2F%28x-2%29 ALIGN=MIDDLE  ALT=\"B%2F%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%2F%28x-3%29 ALIGN=MIDDLE  ALT=\"C%2F%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%5E2-6x%2B6%29%2F%28x-1%29%28x-2%29%28x-3%29 ALIGN=MIDDLE  ALT=\"%282x%5E2-6x%2B6%29%2F%28x-1%29%28x-2%29%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #839337 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=839337\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%2F%28x-1%29%2BB%2F%28x-2%29%2BC%2F%28x-3%29=%282x%5E2-6x%2B6%29%2F%28%28x-1%29%28x-2%29%28x-3%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29%28x-2%29%28x-3%29%2A%28A%2F%28x-1%29%2BB%2F%28x-2%29%2BC%2F%28x-3%29%29=%28x-1%29%28x-2%29%28x-3%29%2A%28%282x%5E2-6x%2B6%29%2F%28%28x-1%29%28x-2%29%28x-3%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by the LCD to clear out fractions \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%28x-2%29%28x-3%29%2BB%28x-1%29%28x-3%29%2BC%28x-1%29%28x-2%29=2x%5E2-6x%2B6 ALIGN=MIDDLE  ALT=\"A%28x-2%29%28x-3%29%2BB%28x-1%29%28x-3%29%2BC%28x-1%29%28x-2%29=2x%5E2-6x%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%28x%5E2-5x%2B6%29%2BB%28x%5E2-4x%2B3%29%2BC%28x%5E2-3x%2B2%29=2x%5E2-6x%2B6 ALIGN=MIDDLE  ALT=\"A%28x%5E2-5x%2B6%29%2BB%28x%5E2-4x%2B3%29%2BC%28x%5E2-3x%2B2%29=2x%5E2-6x%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28Ax%5E2%2BBx%5E2%2BCx%5E2%29%2B%28-5Ax-4Bx-3Cx%29%2B%286A%2B3B%2B2C%29=2x%5E2-6x%2B6 ALIGN=MIDDLE  ALT=\"%28Ax%5E2%2BBx%5E2%2BCx%5E2%29%2B%28-5Ax-4Bx-3Cx%29%2B%286A%2B3B%2B2C%29=2x%5E2-6x%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28A%2BB%2BC%29x%5E2%2B%28-5A-4B-3C%29x%2B%286A%2B3B%2B2C%29=2x%5E2-6x%2B6 ALIGN=MIDDLE  ALT=\"%28A%2BB%2BC%29x%5E2%2B%28-5A-4B-3C%29x%2B%286A%2B3B%2B2C%29=2x%5E2-6x%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Equate corresponding terms<BR>\n" );
document.write( "(A+B+C)x^2 = 2x^2 leads to A+B+C = 2<BR>\n" );
document.write( "(-5A-4B-3C)x = -6x leads to -5A-4B-3C = -6<BR>\n" );
document.write( "6A+3B+2C = 6\r<BR>\n" );
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document.write( "The task is to solve this system of equations<BR>\n" );
document.write( "A+B+C = 2<BR>\n" );
document.write( "-5A-4B-3C = -6<BR>\n" );
document.write( "6A+3B+2C = 6\r<BR>\n" );
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document.write( "Use either elimination, substitution, or <a  rel=nofollow HREF=\"https://www.algebra.com/algebra/homework/coordinate/Linear-systems.faq.question.1203611.html\">matrix row reduction</a>. \r<BR>\n" );
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document.write( "I'll skip the steps for this part, but the answers should be:<BR>\n" );
document.write( "<font color=red>A = 1<BR>\n" );
document.write( "B = -2<BR>\n" );
document.write( "C = 3</font>\r<BR>\n" );
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document.write( "Therefore,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%2F%28x-1%29%2BB%2F%28x-2%29%2BC%2F%28x-3%29=%282x%5E2-6x%2B6%29%2F%28%28x-1%29%28x-2%29%28x-3%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "updates to<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28x-1%29-2%2F%28x-2%29%2B3%2F%28x-3%29=%282x%5E2-6x%2B6%29%2F%28%28x-1%29%28x-2%29%28x-3%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "It is an identity that is true for nearly all real numbers x but <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%3C%3E+1 ALIGN=MIDDLE  ALT=\"x+%3C%3E+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%3C%3E+2 ALIGN=MIDDLE  ALT=\"x+%3C%3E+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%3C%3E+3 ALIGN=MIDDLE  ALT=\"x+%3C%3E+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > (to avoid division by zero errors).\r<BR>\n" );
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document.write( "WolframAlpha can be used to confirm the answer.<BR>\n" );
document.write( "GeoGebra's CAS feature can also be used.<BR>\n" );
document.write( "There are many other online calculators that offer the same features.\r<BR>\n" );
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document.write( "A different approach can be found here:<BR>\n" );
document.write( "<a  rel=nofollow HREF=\"https://www.algebra.com/algebra/homework/expressions/expressions.faq.question.1196220.html\">https://www.algebra.com/algebra/homework/expressions/expressions.faq.question.1196220.html</a><BR>\n" );
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