document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=195562>Question 195562</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0395937760/algebrahomeworkh>McDougal Littell Algebra 1</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this equation: 2+ 8/x-5=x+5/x^2-25 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #146676 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=146676\">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=2%2B8%2F%28x-5%29=%28x%2B5%29%2F%28x%5E2-25%29 ALIGN=MIDDLE  ALT=\"2%2B8%2F%28x-5%29=%28x%2B5%29%2F%28x%5E2-25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2B8%2F%28x-5%29=%28x%2B5%29%2F%28%28x-5%29%28x%2B5%29%29 ALIGN=MIDDLE  ALT=\"2%2B8%2F%28x-5%29=%28x%2B5%29%2F%28%28x-5%29%28x%2B5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor. Take note that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C%3E-5 ALIGN=MIDDLE  ALT=\"x%3C%3E-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C%3E5 ALIGN=MIDDLE  ALT=\"x%3C%3E5\"   DISABLED_style= \"max-width:90%; height:auto;\" > (these values cause a division by zero)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28x-5%29%28x%2B5%29%2Bcross%28%28x-5%29%29%28x%2B5%29%288%2Fcross%28%28x-5%29%29%29=cross%28%28x-5%29%28x%2B5%29%29%28%28x%2B5%29%2F%28cross%28%28x-5%29%28x%2B5%29%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <font size=\"4\"><b>every</b></font> term on both sides by the LCD <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;\" >. Doing this will eliminate all of the fractions.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28x-5%29%28x%2B5%29%2B8%28x%2B5%29=x%2B5 ALIGN=MIDDLE  ALT=\"2%28x-5%29%28x%2B5%29%2B8%28x%2B5%29=x%2B5\"   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=2%28x%5E2-25%29%2B8%28x%2B5%29=x%2B5 ALIGN=MIDDLE  ALT=\"2%28x%5E2-25%29%2B8%28x%2B5%29=x%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" > FOIL\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2-50%2B8x%2B40=x%2B5 ALIGN=MIDDLE  ALT=\"2x%5E2-50%2B8x%2B40=x%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2-50%2B8x%2B40-x-5=0 ALIGN=MIDDLE  ALT=\"2x%5E2-50%2B8x%2B40-x-5=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Get all terms to the left side.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B7x-15=0 ALIGN=MIDDLE  ALT=\"2x%5E2%2B7x-15=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "Notice we have a quadratic equation in the form of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=2 ALIGN=MIDDLE  ALT=\"a=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=7 ALIGN=MIDDLE  ALT=\"b=7\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-15 ALIGN=MIDDLE  ALT=\"c=-15\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Let's use the quadratic formula to solve for x\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the quadratic formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%287%29+%2B-+sqrt%28+%287%29%5E2-4%282%29%28-15%29+%29%29%2F%282%282%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-%287%29+%2B-+sqrt%28+%287%29%5E2-4%282%29%28-15%29+%29%29%2F%282%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=2 ALIGN=MIDDLE  ALT=\"a=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=7 ALIGN=MIDDLE  ALT=\"b=7\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-15 ALIGN=MIDDLE  ALT=\"c=-15\"   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=x+=+%28-7+%2B-+sqrt%28+49-4%282%29%28-15%29+%29%29%2F%282%282%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-7+%2B-+sqrt%28+49-4%282%29%28-15%29+%29%29%2F%282%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7 ALIGN=MIDDLE  ALT=\"7\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=49 ALIGN=MIDDLE  ALT=\"49\"   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=x+=+%28-7+%2B-+sqrt%28+49--120+%29%29%2F%282%282%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-7+%2B-+sqrt%28+49--120+%29%29%2F%282%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%282%29%28-15%29 ALIGN=MIDDLE  ALT=\"4%282%29%28-15%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-120 ALIGN=MIDDLE  ALT=\"-120\"   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=x+=+%28-7+%2B-+sqrt%28+49%2B120+%29%29%2F%282%282%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-7+%2B-+sqrt%28+49%2B120+%29%29%2F%282%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2849--120%29 ALIGN=MIDDLE  ALT=\"sqrt%2849--120%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2849%2B120%29 ALIGN=MIDDLE  ALT=\"sqrt%2849%2B120%29\"   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=x+=+%28-7+%2B-+sqrt%28+169+%29%29%2F%282%282%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-7+%2B-+sqrt%28+169+%29%29%2F%282%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=49 ALIGN=MIDDLE  ALT=\"49\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=120 ALIGN=MIDDLE  ALT=\"120\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=169 ALIGN=MIDDLE  ALT=\"169\"   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=x+=+%28-7+%2B-+sqrt%28+169+%29%29%2F%284%29 ALIGN=MIDDLE  ALT=\"x+=+%28-7+%2B-+sqrt%28+169+%29%29%2F%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   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=x+=+%28-7+%2B-+13%29%2F%284%29 ALIGN=MIDDLE  ALT=\"x+=+%28-7+%2B-+13%29%2F%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=169 ALIGN=MIDDLE  ALT=\"169\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13 ALIGN=MIDDLE  ALT=\"13\"   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=x+=+%28-7+%2B+13%29%2F%284%29 ALIGN=MIDDLE  ALT=\"x+=+%28-7+%2B+13%29%2F%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-7+-+13%29%2F%284%29 ALIGN=MIDDLE  ALT=\"x+=+%28-7+-+13%29%2F%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the expression. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%286%29%2F%284%29 ALIGN=MIDDLE  ALT=\"x+=+%286%29%2F%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=++%28-20%29%2F%284%29 ALIGN=MIDDLE  ALT=\"x+=++%28-20%29%2F%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+3%2F2 ALIGN=MIDDLE  ALT=\"x+=+3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <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;\" > Simplify. \r<BR>\n" );
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document.write( "So the <i>possible</i> answers are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+3%2F2 ALIGN=MIDDLE  ALT=\"x+=+3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <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;\" > \r<BR>\n" );
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document.write( "However, recall that we stated earlier that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C%3E-5 ALIGN=MIDDLE  ALT=\"x%3C%3E-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > (since it causes a division by zero). So <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;\" > is NOT a solution.\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So the only solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+3%2F2 ALIGN=MIDDLE  ALT=\"x+=+3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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