document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=99578>Question 99578</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 2/x+2/x-1=1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #72443 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=72443\">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%2Fx%2B2%2F%28x-1%29=1 ALIGN=MIDDLE  ALT=\"2%2Fx%2B2%2F%28x-1%29=1\"   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=x%28x-1%29%282%2Fx%2B2%2F%28x-1%29%29=x%28x-1%29%281%29 ALIGN=MIDDLE  ALT=\"x%28x-1%29%282%2Fx%2B2%2F%28x-1%29%29=x%28x-1%29%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by the LCD <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28x%2B1%29 ALIGN=MIDDLE  ALT=\"x%28x%2B1%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=2%28x-1%29%2B2x=x%28x-1%29 ALIGN=MIDDLE  ALT=\"2%28x-1%29%2B2x=x%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute and multiply \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-2%2B2x=x%5E2-x ALIGN=MIDDLE  ALT=\"2x-2%2B2x=x%5E2-x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute again\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=x%5E2-5x%2B2 ALIGN=MIDDLE  ALT=\"0=x%5E2-5x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Get all terms to one side\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( "Starting with the general quadratic\r<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;\" >\r<BR>\n" );
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document.write( "the general solution using the quadratic equation is:\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%5E2-4%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;\" >\r<BR>\n" );
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document.write( "So lets solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=x%5E2-5%2Ax%2B2 ALIGN=MIDDLE  ALT=\"0=x%5E2-5%2Ax%2B2\"   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=-5 ALIGN=MIDDLE  ALT=\"b=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=2 ALIGN=MIDDLE  ALT=\"c=2\"   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--5+%2B-+sqrt%28+%28-5%29%5E2-4%2A1%2A2+%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"x+=+%28--5+%2B-+sqrt%28+%28-5%29%5E2-4%2A1%2A2+%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=1, b=-5, and c=2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%285+%2B-+sqrt%28+%28-5%29%5E2-4%2A1%2A2+%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"x+=+%285+%2B-+sqrt%28+%28-5%29%5E2-4%2A1%2A2+%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Negate -5 to get 5\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%285+%2B-+sqrt%28+25-4%2A1%2A2+%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"x+=+%285+%2B-+sqrt%28+25-4%2A1%2A2+%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square -5 to get 25  (note: remember when you square -5, you must square the negative as well. This is because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-5%29%5E2=-5%2A-5=25 ALIGN=MIDDLE  ALT=\"%28-5%29%5E2=-5%2A-5=25\"   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+=+%285+%2B-+sqrt%28+25%2B-8+%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"x+=+%285+%2B-+sqrt%28+25%2B-8+%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2A2%2A1 ALIGN=MIDDLE  ALT=\"-4%2A2%2A1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8 ALIGN=MIDDLE  ALT=\"-8\"   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+=+%285+%2B-+sqrt%28+17+%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"x+=+%285+%2B-+sqrt%28+17+%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms in the radicand (everything under the square root)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%285+%2B-+sqrt%2817%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"x+=+%285+%2B-+sqrt%2817%29%29%2F%282%2A1%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>)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%285+%2B-+sqrt%2817%29%29%2F2 ALIGN=MIDDLE  ALT=\"x+=+%285+%2B-+sqrt%2817%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and 1 to get 2\r<BR>\n" );
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document.write( "So now the expression breaks down into two parts\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%285+%2B+sqrt%2817%29%29%2F2 ALIGN=MIDDLE  ALT=\"x+=+%285+%2B+sqrt%2817%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%285+-+sqrt%2817%29%29%2F2 ALIGN=MIDDLE  ALT=\"x+=+%285+-+sqrt%2817%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now break up the fraction\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%2B5%2F2%2Bsqrt%2817%29%2F2 ALIGN=MIDDLE  ALT=\"x=%2B5%2F2%2Bsqrt%2817%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%2B5%2F2-sqrt%2817%29%2F2 ALIGN=MIDDLE  ALT=\"x=%2B5%2F2-sqrt%2817%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5+%2F+2%2Bsqrt%2817%29%2F2 ALIGN=MIDDLE  ALT=\"x=5+%2F+2%2Bsqrt%2817%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5+%2F+2-sqrt%2817%29%2F2 ALIGN=MIDDLE  ALT=\"x=5+%2F+2-sqrt%2817%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So these expressions approximate to\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4.56155281280883 ALIGN=MIDDLE  ALT=\"x=4.56155281280883\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0.43844718719117 ALIGN=MIDDLE  ALT=\"x=0.43844718719117\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So our solutions are:\r<BR>\n" );
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document.write( "Notice when we graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-5%2Ax%2B2 ALIGN=MIDDLE  ALT=\"x%5E2-5%2Ax%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+500%2C+500%2C+-9.56155281280883%2C+14.5615528128088%2C+-9.56155281280883%2C+14.5615528128088%2C1%2Ax%5E2%2B-5%2Ax%2B2%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "when we use the root finder feature on a calculator, we find that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4.56155281280883 ALIGN=MIDDLE  ALT=\"x=4.56155281280883\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0.43844718719117 ALIGN=MIDDLE  ALT=\"x=0.43844718719117\"   DISABLED_style= \"max-width:90%; height:auto;\" >.So this verifies our answer\r<BR>\n" );
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