document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=277166>Question 277166</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the value of a, b, and c so that i can decompose it to partial functions\r<BR>\n" );
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document.write( "(3x -13)/(6x^2-x-12)\r<BR>\n" );
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document.write( "thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #202126 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=202126\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> find the value of a, b, and c so that i can decompose it to partial functions<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x+-13%29%2F%286x%5E2-x-12%29 ALIGN=MIDDLE  ALT=\"%283x+-13%29%2F%286x%5E2-x-12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x+-+13%29%2F%28%282x-3%29%283x%2B4%29%29 ALIGN=MIDDLE  ALT=\"%283x+-+13%29%2F%28%282x-3%29%283x%2B4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Write the given expression as a sum using A & B<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x+-+13%29%2F%28%282x-3%29%283x%2B4%29%29 ALIGN=MIDDLE  ALT=\"%283x+-+13%29%2F%28%282x-3%29%283x%2B4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%2F%282x-3%29 ALIGN=MIDDLE  ALT=\"A%2F%282x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B%2F%283x%2B4%29 ALIGN=MIDDLE  ALT=\"B%2F%283x%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Multiply by the LCD, (2x-3)(3x+4)<BR>\n" );
document.write( "(2x-3)(3x+4)<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x+-+13%29%2F%28%282x-3%29%283x%2B4%29%29 ALIGN=MIDDLE  ALT=\"%283x+-+13%29%2F%28%282x-3%29%283x%2B4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = (2x-3)(3x+4)<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%2F%282x-3%29 ALIGN=MIDDLE  ALT=\"A%2F%282x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + (2x-3)(3x+4)<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B%2F%283x%2B4%29 ALIGN=MIDDLE  ALT=\"B%2F%283x%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "3x - 13 = A(3x+4) + B(2x-3)<BR>\n" );
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document.write( "3x - 13 = 3xA + 4A + 2xB - 3B<BR>\n" );
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document.write( "3x - 13 - (3A + 2B)x + 4A - 3B<BR>\n" );
document.write( "Coefficients of x are equal<BR>\n" );
document.write( "3A + 2B = 3<BR>\n" );
document.write( "Constants are equal<BR>\n" );
document.write( "4A - 3B = -13<BR>\n" );
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document.write( "Solve for two unknowns using elimination, multiply 1st eq by 3, 2nd eq by 2<BR>\n" );
document.write( "9A + 6B = 9<BR>\n" );
document.write( "8A - 6B =-26<BR>\n" );
document.write( "----------------adding eliminates B, find A<BR>\n" );
document.write( "17A = -17<BR>\n" );
document.write( "A = -1<BR>\n" );
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document.write( "Find B<BR>\n" );
document.write( "3A + 2B = 3<BR>\n" );
document.write( "3(-1) + 2B = 3<BR>\n" );
document.write( "-3 + 2B = 3<BR>\n" );
document.write( "2B = 3 + 3<BR>\n" );
document.write( "2B = 6<BR>\n" );
document.write( "B = 3<BR>\n" );
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document.write( "We have<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x+-+13%29%2F%286x%5E2-x-12%29 ALIGN=MIDDLE  ALT=\"%283x+-+13%29%2F%286x%5E2-x-12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F%282x-3%29 ALIGN=MIDDLE  ALT=\"-1%2F%282x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F%283x%2B4%29 ALIGN=MIDDLE  ALT=\"3%2F%283x%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You should check this by adding the two fractions on the right to see if they equal the expression on the left<BR>\n" );
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