document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=88323>Question 88323</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello, \r<BR>\n" );
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document.write( "I'm having a bit of a difficult time figuring out if I have done this problem correctly, and would greatly appreciate if someone could tell me if I've solved it correctly or if I am way off track, and show me what I need to do. \r<BR>\n" );
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document.write( "Here is the original problem that I have to solve: 9/(x-5) - 1 = 8/(x+5). \r<BR>\n" );
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document.write( "Here's the solution that I've come to: First, I moved 8/x+5 to the left, so that the equation read like this: 9/x-5  -1  -8/x+5 = 0. Then, I moved -1 to the right of the equation, so that it read like this: 9/x-5 - 8/x+5 -1 =0, which I think is the solution to the problem, right? Is there further solving or simplifying involved that I'm overlooking or is my solution correct? \r<BR>\n" );
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document.write( "Thank you very, very much in advance for your help! <BR>\n" );
document.write( "  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #64150 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=64150\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Ok, your first move was good! So you have:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2F%28x-5%29+-+8%2F%28x%2B5%29+-+1+=+0 ALIGN=MIDDLE  ALT=\"9%2F%28x-5%29+-+8%2F%28x%2B5%29+-+1+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now add 1 (move the -1 to the right side) to both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2F%28x-5%29+-+8%2F%28x%2B5%29+=+1 ALIGN=MIDDLE  ALT=\"9%2F%28x-5%29+-+8%2F%28x%2B5%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now add the two fractions on the left side.  The LCD is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-5%29%28x%2B5%29 ALIGN=MIDDLE  ALT=\"%28x-5%29%28x%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > so you now have:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289%28x%2B5%29-8%28x-5%29%29%2F%28x-5%29%28x%2B5%29+=+1 ALIGN=MIDDLE  ALT=\"%289%28x%2B5%29-8%28x-5%29%29%2F%28x-5%29%28x%2B5%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify the numerator.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289x%2B45-8x%2B40%29%2F%28x-5%29%28x%2B5%29+=+1 ALIGN=MIDDLE  ALT=\"%289x%2B45-8x%2B40%29%2F%28x-5%29%28x%2B5%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Continue to simplify.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B85%29%2F%28x-5%29%28x%2B5%29+=+1 ALIGN=MIDDLE  ALT=\"%28x%2B85%29%2F%28x-5%29%28x%2B5%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-5%29%28x%2B5%29 ALIGN=MIDDLE  ALT=\"%28x-5%29%28x%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B85+=+%28x-5%29%28x%2B5%29 ALIGN=MIDDLE  ALT=\"x%2B85+=+%28x-5%29%28x%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Expand the right side.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B85+=+x%5E2-25 ALIGN=MIDDLE  ALT=\"x%2B85+=+x%5E2-25\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B85 ALIGN=MIDDLE  ALT=\"x%2B85\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+x%5E2-x-110 ALIGN=MIDDLE  ALT=\"0+=+x%5E2-x-110\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-x-110+=+0 ALIGN=MIDDLE  ALT=\"x%5E2-x-110+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > This can be factored:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B10%29%28x-11%29+=+0 ALIGN=MIDDLE  ALT=\"%28x%2B10%29%28x-11%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Apply the zero products principle to get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-10 ALIGN=MIDDLE  ALT=\"x+=+-10\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+11 ALIGN=MIDDLE  ALT=\"x+=+11\"   DISABLED_style= \"max-width:90%; height:auto;\" > These are the solutions!<BR>\n" );
document.write( "Let's check the solutions by substituting the solutions, one-by-one into the original equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289%2F%28x-5%29%29-1+=+8%2F%28x%2B5%29 ALIGN=MIDDLE  ALT=\"%289%2F%28x-5%29%29-1+=+8%2F%28x%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Substitute x = -10.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289%2F%28-10-5%29%29-1+=+8%2F%28-10%2B5%29 ALIGN=MIDDLE  ALT=\"%289%2F%28-10-5%29%29-1+=+8%2F%28-10%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289%2F%28-15%29%29+-+1+=+8%2F%28-5%29 ALIGN=MIDDLE  ALT=\"%289%2F%28-15%29%29+-+1+=+8%2F%28-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289%2F%28-15%29%29+-+%28%28-15%29%2F%28-15%29%29+=+8%2F%28-5%29 ALIGN=MIDDLE  ALT=\"%289%2F%28-15%29%29+-+%28%28-15%29%2F%28-15%29%29+=+8%2F%28-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-24%2F15+=+-%288%2F5%29 ALIGN=MIDDLE  ALT=\"-24%2F15+=+-%288%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce the fraction on the left side.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%288%2F5%29+=+-%288%2F5%29 ALIGN=MIDDLE  ALT=\"-%288%2F5%29+=+-%288%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > It checks!<BR>\n" );
document.write( "Try the other solution yourself and see how you do. </SPAN>\n" );
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