document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=110624>Question 110624</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the equation.\r<BR>\n" );
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document.write( "3/x+3/x-5=3x-12/x-5 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #80669 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=80669\">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=3%2Fx%2B3%2F%28x-5%29=%283x-12%29%2F%28x-5%29 ALIGN=MIDDLE  ALT=\"3%2Fx%2B3%2F%28x-5%29=%283x-12%29%2F%28x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Step 1 is to look at the domain of the function.  Note that either x = 0 or x = 5 results in a 0 denominator, so the domain is all real except 0 and 5.<BR>\n" );
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document.write( "Step 2 is to find the common denominator.  The only factors we have are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-5 ALIGN=MIDDLE  ALT=\"x-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so the only common denominator is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28x-5%29 ALIGN=MIDDLE  ALT=\"x%28x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28x-5%29%2Fx%28x-5%29%2B3x%2Fx%28x-5%29=x%283x-12%29%2Fx%28x-5%29 ALIGN=MIDDLE  ALT=\"3%28x-5%29%2Fx%28x-5%29%2B3x%2Fx%28x-5%29=x%283x-12%29%2Fx%28x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now we need to simplify and collect like terms.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x-15%2B3x%29%2Fx%28x-5%29=%283x%5E2-12x%29%2Fx%28x-5%29 ALIGN=MIDDLE  ALT=\"%283x-15%2B3x%29%2Fx%28x-5%29=%283x%5E2-12x%29%2Fx%28x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x-15%2B3x%29=%283x%5E2-12x%29 ALIGN=MIDDLE  ALT=\"%283x-15%2B3x%29=%283x%5E2-12x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, after multiplication by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28x-5%29 ALIGN=MIDDLE  ALT=\"x%28x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x-15-3x%5E2%2B12x=0 ALIGN=MIDDLE  ALT=\"6x-15-3x%5E2%2B12x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2-18x%2B15=0 ALIGN=MIDDLE  ALT=\"3x%5E2-18x%2B15=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, after collecting terms and multiplying by -1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-6x%2B5=0 ALIGN=MIDDLE  ALT=\"x%5E2-6x%2B5=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, after dividing by 3<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-5%29%28x-1%29=0 ALIGN=MIDDLE  ALT=\"%28x-5%29%28x-1%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, after factoring (given the difficulty level of this problem, I'm assuming you know how to factor a 2nd degree polynomial.  If you need help with that, write me a note.<BR>\n" );
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document.write( "So,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5 ALIGN=MIDDLE  ALT=\"x=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, BUT remember that 5 was excluded from the domain, therefore the only solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
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document.write( "Hope this helps<BR>\n" );
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document.write( "In the graph below, note the curve is asymptotic to the y-axis and there is a discontinuity at 5.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-10%2C10%2C-10%2C10%2C3%2Fx%2B3%2F%28x-5%29-%283x-12%29%2F%28x-5%29%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-10%2C10%2C-10%2C10%2C3%2Fx%2B3%2F%28x-5%29-%283x-12%29%2F%28x-5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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