document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=103817>Question 103817</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve.   <BR>\n" );
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document.write( "9/x-5  -1 = 8/x+5<BR>\n" );
document.write( " Can anyone help me figure these fractions out, so i CAN HAVE A FORMULA for future references, the slashes are fraction bars. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #75480 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=75480\">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=9%2F%28x-5+%29-1+=+8%2F%28x%2B5%29 ALIGN=MIDDLE  ALT=\"9%2F%28x-5+%29-1+=+8%2F%28x%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  simplifies to <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;\" >\r<BR>\n" );
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document.write( "The least common denominator 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;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%28x%2B5%29%2F%28x-5%29%28x%2B5%29+-++8%28x-5%29%2F%28x-5%29%28x%2B5%29-+1%28x-5%29%28x%2B5%29%2F+%28x-5%29%28x%2B5%29+=+0 ALIGN=MIDDLE   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=%289%28x%2B5%29+-+8%28x-5%29+-+1%28x-5%29%28x%2B5%29%29%2F%28x-5%29%28x%2B5%29+=+0 ALIGN=MIDDLE  ALT=\"%289%28x%2B5%29+-+8%28x-5%29+-+1%28x-5%29%28x%2B5%29%29%2F%28x-5%29%28x%2B5%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > now both sides multiply 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;\" > and you will have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289%28x%2B5%29+-+8%28x-5%29+-+1%28x-5%29%28x%2B5%29%29%2F%28x-5%29%28x%2B5%29+=+0 ALIGN=MIDDLE  ALT=\"%289%28x%2B5%29+-+8%28x-5%29+-+1%28x-5%29%28x%2B5%29%29%2F%28x-5%29%28x%2B5%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > /* <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;\" > \r<BR>\n" );
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document.write( "this will eliminate denominator, and you will have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289%28x%2B5%29+-+8%28x-5%29+-+1%28x-5%29%28x%2B5%29%29+=+0 ALIGN=MIDDLE  ALT=\"%289%28x%2B5%29+-+8%28x-5%29+-+1%28x-5%29%28x%2B5%29%29+=+0\"   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=9x+%2B+45+-+8x+%2B+40+-+%28x%5E2%2B+5x+-5x+-25%29+=+0 ALIGN=MIDDLE  ALT=\"9x+%2B+45+-+8x+%2B+40+-+%28x%5E2%2B+5x+-5x+-25%29+=+0\"   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+%2B+85+-+x%5E2+%2B+25+=+0 ALIGN=MIDDLE  ALT=\"x+%2B+85+-+x%5E2+%2B+25+=+0\"   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%5E2+%2B+x+%2B+110+=+0 ALIGN=MIDDLE  ALT=\"-+x%5E2+%2B+x+%2B+110+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "now you can use quadratic formula to find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x1 ALIGN=MIDDLE  ALT=\"x1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x2 ALIGN=MIDDLE  ALT=\"x2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then you can graf it\r<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=quadratic_formula.solver>Quadratic Formula</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Let's use the quadratic formula to solve for x:<BR><BR>\n" );
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document.write( "  Starting with the general quadratic<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  the general solution using the quadratic equation is:<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%5E2-4%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" );
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document.write( "  So lets solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%5E2%2Bx%2B110=0 ALIGN=MIDDLE  ALT=\"-x%5E2%2Bx%2B110=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( notice <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-1 ALIGN=MIDDLE  ALT=\"a=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=1 ALIGN=MIDDLE  ALT=\"b=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=110 ALIGN=MIDDLE  ALT=\"c=110\"   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=x+=+%28-1+%2B-+sqrt%28+%281%29%5E2-4%2A-1%2A110+%29%29%2F%282%2A-1%29 ALIGN=MIDDLE  ALT=\"x+=+%28-1+%2B-+sqrt%28+%281%29%5E2-4%2A-1%2A110+%29%29%2F%282%2A-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=-1, b=1, and c=110<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-1+%2B-+sqrt%28+1-4%2A-1%2A110+%29%29%2F%282%2A-1%29 ALIGN=MIDDLE  ALT=\"x+=+%28-1+%2B-+sqrt%28+1-4%2A-1%2A110+%29%29%2F%282%2A-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 1 to get 1  <BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-1+%2B-+sqrt%28+1%2B440+%29%29%2F%282%2A-1%29 ALIGN=MIDDLE  ALT=\"x+=+%28-1+%2B-+sqrt%28+1%2B440+%29%29%2F%282%2A-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2A110%2A-1 ALIGN=MIDDLE  ALT=\"-4%2A110%2A-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=440 ALIGN=MIDDLE  ALT=\"440\"   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=x+=+%28-1+%2B-+sqrt%28+441+%29%29%2F%282%2A-1%29 ALIGN=MIDDLE  ALT=\"x+=+%28-1+%2B-+sqrt%28+441+%29%29%2F%282%2A-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms in the radicand (everything under the square root)<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-1+%2B-+21%29%2F%282%2A-1%29 ALIGN=MIDDLE  ALT=\"x+=+%28-1+%2B-+21%29%2F%282%2A-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify the square root (note: If you need help with simplifying the square root, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver> solver</a>)<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-1+%2B-+21%29%2F-2 ALIGN=MIDDLE  ALT=\"x+=+%28-1+%2B-+21%29%2F-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and -1 to get -2<BR>\n" );
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document.write( "  So now the expression breaks down into two parts<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-1+%2B+21%29%2F-2 ALIGN=MIDDLE  ALT=\"x+=+%28-1+%2B+21%29%2F-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-1+-+21%29%2F-2 ALIGN=MIDDLE  ALT=\"x+=+%28-1+-+21%29%2F-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  Lets look at the first part:<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-1+%2B+21%29%2F-2 ALIGN=MIDDLE  ALT=\"x=%28-1+%2B+21%29%2F-2\"   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=x=20%2F-2 ALIGN=MIDDLE  ALT=\"x=20%2F-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add the terms in the numerator<BR>\n" );
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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;\" > Divide<BR>\n" );
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document.write( "  So one answer is<BR>\n" );
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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;\" ><BR>\n" );
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document.write( "  Now lets look at the second part:<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-1+-+21%29%2F-2 ALIGN=MIDDLE  ALT=\"x=%28-1+-+21%29%2F-2\"   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=x=-22%2F-2 ALIGN=MIDDLE  ALT=\"x=-22%2F-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract the terms in the numerator<BR>\n" );
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document.write( "  <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;\" > Divide<BR>\n" );
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document.write( "  So another answer is<BR>\n" );
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document.write( "  <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;\" ><BR>\n" );
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document.write( "  So our solutions are:<BR>\n" );
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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;\" ><BR>\n" );
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