document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=413652>Question 413652</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you help me solve the equation by using the Lowest Common Denominator? The problem is <BR>\n" );
document.write( "5/x^2+x-6 = 2+ x-3/x-2\r<BR>\n" );
document.write( "\n" );
document.write( "Can you show me step by step how to get the answer? My teacher can't teach and the homework hotline is closed. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #290320 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=290320\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F%28x%5E2%2Bx-6%29 ALIGN=MIDDLE  ALT=\"5%2F%28x%5E2%2Bx-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 2 + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%2F%28x-2%29 ALIGN=MIDDLE  ALT=\"%28x-3%29%2F%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "Factor the 1st denominator<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F%28%28x%2B3%29%28x-2%29%29 ALIGN=MIDDLE  ALT=\"5%2F%28%28x%2B3%29%28x-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 2 + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%2F%28x-2%29 ALIGN=MIDDLE  ALT=\"%28x-3%29%2F%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "the common denominator consists of the factors of both denominators<BR>\n" );
document.write( "the common denominator is (x+3)(x-2)*<BR>\n" );
document.write( "Multiply each term by the common denominator<BR>\n" );
document.write( "(x+3)(x-2)*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F%28%28x%2B3%29%28x-2%29%29 ALIGN=MIDDLE  ALT=\"5%2F%28%28x%2B3%29%28x-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = (x+3)(x-2)*2 + (x+3)(x-2)*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%2F%28x-2%29 ALIGN=MIDDLE  ALT=\"%28x-3%29%2F%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Cancel out the denominators that you can and you have:<BR>\n" );
document.write( "5 = 2(x+3)(x-2) + (x+3)(x-3)<BR>\n" );
document.write( "FOIL<BR>\n" );
document.write( "5 = 2(x^2 - 2x + 3x - 6) + (x^2 -3x + 3x - 9)<BR>\n" );
document.write( "5 = 2(x^2 + x - 6) + (x^2-9)<BR>\n" );
document.write( "5 = 2x^2 + 2x - 12 + x^2 - 9<BR>\n" );
document.write( "Combine like terms<BR>\n" );
document.write( "0 = 2x^2 + x^2 + 2x - 12 - 9 - 5<BR>\n" );
document.write( "a quadratic equation<BR>\n" );
document.write( "3x^2 + 2x - 26 = 0<BR>\n" );
document.write( "You have to solve this equation using the quadratic formula<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "In this equation; a=3; b=2; c=-26<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-2+%2B-+sqrt%282%5E2-4%2A3%2A-26+%29%29%2F%282%2A3%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-2+%2B-+sqrt%282%5E2-4%2A3%2A-26+%29%29%2F%282%2A3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-2+%2B-+sqrt%284-%28-312%29+%29%29%2F%286%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-2+%2B-+sqrt%284-%28-312%29+%29%29%2F%286%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-2+%2B-+sqrt%284+%2B+312+%29%29%2F%286%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-2+%2B-+sqrt%284+%2B+312+%29%29%2F%286%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-2+%2B-+sqrt%28316+%29%29%2F%286%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-2+%2B-+sqrt%28316+%29%29%2F%286%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Two solutions<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-2+%2B+17.776%29%2F%286%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-2+%2B+17.776%29%2F%286%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15.776%2F6 ALIGN=MIDDLE  ALT=\"15.776%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = 2.63<BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-2+-+17.776%29%2F%286%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-2+-+17.776%29%2F%286%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=19.776%2F6 ALIGN=MIDDLE  ALT=\"19.776%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = -3.296<BR>\n" );
document.write( ":<BR>\n" );
document.write( "You job is to check both these solutions in the original equation\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );