document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=167696>Question 167696</A>: <I><SPAN STYLE=\"word-break: break-all;\"> x+1/1 + x - 1/3-x = 6/35 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #123610 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=123610\">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=%28x%2B1%29%2F%281%2Bx%29-%281%29%2F%283-x%29=%286%29%2F%2835%29 ALIGN=MIDDLE  ALT=\"%28x%2B1%29%2F%281%2Bx%29-%281%29%2F%283-x%29=%286%29%2F%2835%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=35cross%28%281%2Bx%29%29%283-x%29%28%28x%2B1%29%2Fcross%28%281%2Bx%29%29%29-35%281%2Bx%29cross%28%283-x%29%29%28%281%29%2Fcross%28%283-x%29%29%29=cross%2835%29%281%2Bx%29%283-x%29%28%286%29%2Fcross%2835%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=35%281%2Bx%29%283-x%29 ALIGN=MIDDLE  ALT=\"35%281%2Bx%29%283-x%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=35%283-x%29%28x%2B1%29-35%281%2Bx%29=6%281%2Bx%29%283-x%29 ALIGN=MIDDLE  ALT=\"35%283-x%29%28x%2B1%29-35%281%2Bx%29=6%281%2Bx%29%283-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply and simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=35%283%2B2x-x%5E2%29-35%281%2Bx%29=6%283%2B2x-x%5E2%29 ALIGN=MIDDLE  ALT=\"35%283%2B2x-x%5E2%29-35%281%2Bx%29=6%283%2B2x-x%5E2%29\"   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=105%2B70x-35x%5E2-35-35x=18%2B12x-6x%5E2 ALIGN=MIDDLE  ALT=\"105%2B70x-35x%5E2-35-35x=18%2B12x-6x%5E2\"   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=-35x%5E2%2B35x%2B70=-6x%5E2%2B12x%2B18 ALIGN=MIDDLE  ALT=\"-35x%5E2%2B35x%2B70=-6x%5E2%2B12x%2B18\"   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=-35x%5E2%2B35x%2B70%2B6x%5E2-12x-18=0 ALIGN=MIDDLE  ALT=\"-35x%5E2%2B35x%2B70%2B6x%5E2-12x-18=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=-29x%5E2%2B23x%2B52=0 ALIGN=MIDDLE  ALT=\"-29x%5E2%2B23x%2B52=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=-29 ALIGN=MIDDLE  ALT=\"a=-29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=23 ALIGN=MIDDLE  ALT=\"b=23\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=52 ALIGN=MIDDLE  ALT=\"c=52\"   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-%2823%29+%2B-+sqrt%28+%2823%29%5E2-4%28-29%29%2852%29+%29%29%2F%282%28-29%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-%2823%29+%2B-+sqrt%28+%2823%29%5E2-4%28-29%29%2852%29+%29%29%2F%282%28-29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-29 ALIGN=MIDDLE  ALT=\"a=-29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=23 ALIGN=MIDDLE  ALT=\"b=23\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=52 ALIGN=MIDDLE  ALT=\"c=52\"   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+=+%28-23+%2B-+sqrt%28+529-4%28-29%29%2852%29+%29%29%2F%282%28-29%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-23+%2B-+sqrt%28+529-4%28-29%29%2852%29+%29%29%2F%282%28-29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=23 ALIGN=MIDDLE  ALT=\"23\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=529 ALIGN=MIDDLE  ALT=\"529\"   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+=+%28-23+%2B-+sqrt%28+529--6032+%29%29%2F%282%28-29%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-23+%2B-+sqrt%28+529--6032+%29%29%2F%282%28-29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28-29%29%2852%29 ALIGN=MIDDLE  ALT=\"4%28-29%29%2852%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6032 ALIGN=MIDDLE  ALT=\"-6032\"   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+=+%28-23+%2B-+sqrt%28+529%2B6032+%29%29%2F%282%28-29%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-23+%2B-+sqrt%28+529%2B6032+%29%29%2F%282%28-29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28529--6032%29 ALIGN=MIDDLE  ALT=\"sqrt%28529--6032%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28529%2B6032%29 ALIGN=MIDDLE  ALT=\"sqrt%28529%2B6032%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+=+%28-23+%2B-+sqrt%28+6561+%29%29%2F%282%28-29%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-23+%2B-+sqrt%28+6561+%29%29%2F%282%28-29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=529 ALIGN=MIDDLE  ALT=\"529\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6032 ALIGN=MIDDLE  ALT=\"6032\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6561 ALIGN=MIDDLE  ALT=\"6561\"   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+=+%28-23+%2B-+sqrt%28+6561+%29%29%2F%28-58%29 ALIGN=MIDDLE  ALT=\"x+=+%28-23+%2B-+sqrt%28+6561+%29%29%2F%28-58%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=-29 ALIGN=MIDDLE  ALT=\"-29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-58 ALIGN=MIDDLE  ALT=\"-58\"   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+=+%28-23+%2B-+81%29%2F%28-58%29 ALIGN=MIDDLE  ALT=\"x+=+%28-23+%2B-+81%29%2F%28-58%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=6561 ALIGN=MIDDLE  ALT=\"6561\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=81 ALIGN=MIDDLE  ALT=\"81\"   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+=+%28-23+%2B+81%29%2F%28-58%29 ALIGN=MIDDLE  ALT=\"x+=+%28-23+%2B+81%29%2F%28-58%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-23+-+81%29%2F%28-58%29 ALIGN=MIDDLE  ALT=\"x+=+%28-23+-+81%29%2F%28-58%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+=+%2858%29%2F%28-58%29 ALIGN=MIDDLE  ALT=\"x+=+%2858%29%2F%28-58%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=++%28-104%29%2F%28-58%29 ALIGN=MIDDLE  ALT=\"x+=++%28-104%29%2F%28-58%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+=+-1 ALIGN=MIDDLE  ALT=\"x+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+52%2F29 ALIGN=MIDDLE  ALT=\"x+=+52%2F29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify. \r<BR>\n" );
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document.write( "So the possible answers are <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;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+52%2F29 ALIGN=MIDDLE  ALT=\"x+=+52%2F29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "However, if you plug in <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;\" >, then you will get a division by zero. So the only answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+52%2F29 ALIGN=MIDDLE  ALT=\"x+=+52%2F29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So the solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+52%2F29 ALIGN=MIDDLE  ALT=\"x+=+52%2F29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which approximates to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1.793 ALIGN=MIDDLE  ALT=\"x=1.793\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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