document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=270261>Question 270261</A>: <I><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F%282x%2B2%29%2B1%2F4=-1%2F%28x%2B2%29 ALIGN=MIDDLE  ALT=\"x%2F%282x%2B2%29%2B1%2F4=-1%2F%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #198012 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=198012\">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=x%2F%282x%2B2%29%2B1%2F4=-1%2F%28x%2B2%29 ALIGN=MIDDLE  ALT=\"x%2F%282x%2B2%29%2B1%2F4=-1%2F%28x%2B2%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=x%2F%282%28x%2B1%29%29%2B1%2F4=-1%2F%28x%2B2%29 ALIGN=MIDDLE  ALT=\"x%2F%282%28x%2B1%29%29%2B1%2F4=-1%2F%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor the first denominator.\r<BR>\n" );
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document.write( "Take note that the LCD is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28x%2B1%29%28x%2B2%29 ALIGN=MIDDLE  ALT=\"4%28x%2B1%29%28x%2B2%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=cross%284%29%5E2cross%28%28x%2B1%29%29%28x%2B2%29%28x%2F%28cross%282%29cross%28%28x%2B1%29%29%29%29%2Bcross%284%29%28x%2B1%29%28x%2B2%29%281%2Fcross%284%29%29=4%28x%2B1%29cross%28%28x%2B2%29%29%28-1%2Fcross%28%28x%2B2%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply EVERY term by the LCD <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28x%2B1%29%28x%2B2%29 ALIGN=MIDDLE  ALT=\"4%28x%2B1%29%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to eliminate 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%2B2%29x%2B%28x%2B1%29%28x%2B2%29=4%28x%2B1%29%28-1%29 ALIGN=MIDDLE  ALT=\"2%28x%2B2%29x%2B%28x%2B1%29%28x%2B2%29=4%28x%2B1%29%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%28x%2B2%29%2B%28x%2B1%29%28x%2B2%29=4%28-1%29%28x%2B1%29 ALIGN=MIDDLE  ALT=\"2x%28x%2B2%29%2B%28x%2B1%29%28x%2B2%29=4%28-1%29%28x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%28x%2B2%29%2B%28x%2B1%29%28x%2B2%29=-4%28x%2B1%29 ALIGN=MIDDLE  ALT=\"2x%28x%2B2%29%2B%28x%2B1%29%28x%2B2%29=-4%28x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B4x%2B%28x%2B1%29%28x%2B2%29=-4x-4 ALIGN=MIDDLE  ALT=\"2x%5E2%2B4x%2B%28x%2B1%29%28x%2B2%29=-4x-4\"   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%2B4x%2Bx%5E2%2B3x%2B2=-4x-4 ALIGN=MIDDLE  ALT=\"2x%5E2%2B4x%2Bx%5E2%2B3x%2B2=-4x-4\"   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%2B4x%2Bx%5E2%2B3x%2B2%2B4x%2B4=0 ALIGN=MIDDLE  ALT=\"2x%5E2%2B4x%2Bx%5E2%2B3x%2B2%2B4x%2B4=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Get every term to one side.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2%2B11x%2B6=0 ALIGN=MIDDLE  ALT=\"3x%5E2%2B11x%2B6=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "Now let's use the quadratic formula to solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2%2B11x%2B6=0 ALIGN=MIDDLE  ALT=\"3x%5E2%2B11x%2B6=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\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=3%2Ax%5E2%2B11%2Ax%2B6=0 ALIGN=MIDDLE  ALT=\"3%2Ax%5E2%2B11%2Ax%2B6=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( notice <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=3 ALIGN=MIDDLE  ALT=\"a=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=11 ALIGN=MIDDLE  ALT=\"b=11\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=6 ALIGN=MIDDLE  ALT=\"c=6\"   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+=+%28-11+%2B-+sqrt%28+%2811%29%5E2-4%2A3%2A6+%29%29%2F%282%2A3%29 ALIGN=MIDDLE  ALT=\"x+=+%28-11+%2B-+sqrt%28+%2811%29%5E2-4%2A3%2A6+%29%29%2F%282%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=3, b=11, and c=6<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-11+%2B-+sqrt%28+121-4%2A3%2A6+%29%29%2F%282%2A3%29 ALIGN=MIDDLE  ALT=\"x+=+%28-11+%2B-+sqrt%28+121-4%2A3%2A6+%29%29%2F%282%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 11 to get 121  <BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-11+%2B-+sqrt%28+121%2B-72+%29%29%2F%282%2A3%29 ALIGN=MIDDLE  ALT=\"x+=+%28-11+%2B-+sqrt%28+121%2B-72+%29%29%2F%282%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2A6%2A3 ALIGN=MIDDLE  ALT=\"-4%2A6%2A3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-72 ALIGN=MIDDLE  ALT=\"-72\"   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+=+%28-11+%2B-+sqrt%28+49+%29%29%2F%282%2A3%29 ALIGN=MIDDLE  ALT=\"x+=+%28-11+%2B-+sqrt%28+49+%29%29%2F%282%2A3%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+=+%28-11+%2B-+7%29%2F%282%2A3%29 ALIGN=MIDDLE  ALT=\"x+=+%28-11+%2B-+7%29%2F%282%2A3%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+=+%28-11+%2B-+7%29%2F6 ALIGN=MIDDLE  ALT=\"x+=+%28-11+%2B-+7%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and 3 to get 6<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+=+%28-11+%2B+7%29%2F6 ALIGN=MIDDLE  ALT=\"x+=+%28-11+%2B+7%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-11+-+7%29%2F6 ALIGN=MIDDLE  ALT=\"x+=+%28-11+-+7%29%2F6\"   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=%28-11+%2B+7%29%2F6 ALIGN=MIDDLE  ALT=\"x=%28-11+%2B+7%29%2F6\"   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=-4%2F6 ALIGN=MIDDLE  ALT=\"x=-4%2F6\"   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=-2%2F3 ALIGN=MIDDLE  ALT=\"x=-2%2F3\"   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( "  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=%28-11+-+7%29%2F6 ALIGN=MIDDLE  ALT=\"x=%28-11+-+7%29%2F6\"   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=-18%2F6 ALIGN=MIDDLE  ALT=\"x=-18%2F6\"   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=-3 ALIGN=MIDDLE  ALT=\"x=-3\"   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( "  So our solutions are:<BR>\n" );
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document.write( "So the solutions to the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F%282x%2B2%29%2B1%2F4=-1%2F%28x%2B2%29 ALIGN=MIDDLE  ALT=\"x%2F%282x%2B2%29%2B1%2F4=-1%2F%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > are\r<BR>\n" );
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