document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=118765>Question 118765</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the root(s) of x-2/x-4 + 2= 2x+3/5<BR>\n" );
document.write( "Can someone please tell me why I lost marks :(<BR>\n" );
document.write( " I Did : 5(x-2)+2(x-4)=(2x+3)(x-4)<BR>\n" );
document.write( "         5x-10+2x-8=2x^2-8x+3x-12<BR>\n" );
document.write( "         7x-18=2x62-5x-12<BR>\n" );
document.write( "         7x-18+-2x^2+5x+12=0<BR>\n" );
document.write( "         12x-6+-2x^2=0<BR>\n" );
document.write( "         x^2+-6x+3=0<BR>\n" );
document.write( " Then I used the quadratic formula and got:<BR>\n" );
document.write( "      x=6+-2sqrt6/2<BR>\n" );
document.write( "      x=3=-sqrt6<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #86904 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=86904\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You made a mistake in your first step. Remember, the LCD is 5(x-4). You multiplied the second term 2 by only the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-4 ALIGN=MIDDLE  ALT=\"x-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and forgot the 5. So you should have\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%28x-2%29%2B2%2Ahighlight%285%29%2A%28x-4%29=%282x%2B3%29%28x-4%29 ALIGN=MIDDLE  ALT=\"5%28x-2%29%2B2%2Ahighlight%285%29%2A%28x-4%29=%282x%2B3%29%28x-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%28x-2%29%2B10%28x-4%29=%282x%2B3%29%28x-4%29 ALIGN=MIDDLE  ALT=\"5%28x-2%29%2B10%28x-4%29=%282x%2B3%29%28x-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x-10%2B10x-40=%282x%2B3%29%28x-4%29 ALIGN=MIDDLE  ALT=\"5x-10%2B10x-40=%282x%2B3%29%28x-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x-10%2B10x-40=2x%5E2-5x-12 ALIGN=MIDDLE  ALT=\"5x-10%2B10x-40=2x%5E2-5x-12\"   DISABLED_style= \"max-width:90%; height:auto;\" > Foil\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x-10%2B10x-40-2x%5E2%2B5x%2B12=0 ALIGN=MIDDLE  ALT=\"5x-10%2B10x-40-2x%5E2%2B5x%2B12=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Get all terms to one side\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2x%5E2%2B20x-38=0 ALIGN=MIDDLE  ALT=\"-2x%5E2%2B20x-38=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Let's use the quadratic formula to solve for x:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Starting with the general quadratic\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
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" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the general solution using the quadratic equation is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
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" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So lets solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%2Ax%5E2%2B20%2Ax-38=0 ALIGN=MIDDLE  ALT=\"-2%2Ax%5E2%2B20%2Ax-38=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( notice <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=20 ALIGN=MIDDLE  ALT=\"b=20\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-38 ALIGN=MIDDLE  ALT=\"c=-38\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-20+%2B-+sqrt%28+%2820%29%5E2-4%2A-2%2A-38+%29%29%2F%282%2A-2%29 ALIGN=MIDDLE  ALT=\"x+=+%28-20+%2B-+sqrt%28+%2820%29%5E2-4%2A-2%2A-38+%29%29%2F%282%2A-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=-2, b=20, and c=-38\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-20+%2B-+sqrt%28+400-4%2A-2%2A-38+%29%29%2F%282%2A-2%29 ALIGN=MIDDLE  ALT=\"x+=+%28-20+%2B-+sqrt%28+400-4%2A-2%2A-38+%29%29%2F%282%2A-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 20 to get 400  \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-20+%2B-+sqrt%28+400%2B-304+%29%29%2F%282%2A-2%29 ALIGN=MIDDLE  ALT=\"x+=+%28-20+%2B-+sqrt%28+400%2B-304+%29%29%2F%282%2A-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2A-38%2A-2 ALIGN=MIDDLE  ALT=\"-4%2A-38%2A-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-304 ALIGN=MIDDLE  ALT=\"-304\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-20+%2B-+sqrt%28+96+%29%29%2F%282%2A-2%29 ALIGN=MIDDLE  ALT=\"x+=+%28-20+%2B-+sqrt%28+96+%29%29%2F%282%2A-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms in the radicand (everything under the square root)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-20+%2B-+4%2Asqrt%286%29%29%2F%282%2A-2%29 ALIGN=MIDDLE  ALT=\"x+=+%28-20+%2B-+4%2Asqrt%286%29%29%2F%282%2A-2%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" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-20+%2B-+4%2Asqrt%286%29%29%2F-4 ALIGN=MIDDLE  ALT=\"x+=+%28-20+%2B-+4%2Asqrt%286%29%29%2F-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and -2 to get -4\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So now the expression breaks down into two parts\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-20+%2B+4%2Asqrt%286%29%29%2F-4 ALIGN=MIDDLE  ALT=\"x+=+%28-20+%2B+4%2Asqrt%286%29%29%2F-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-20+-+4%2Asqrt%286%29%29%2F-4 ALIGN=MIDDLE  ALT=\"x+=+%28-20+-+4%2Asqrt%286%29%29%2F-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now break up the fraction\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-20%2F-4%2B4%2Asqrt%286%29%2F-4 ALIGN=MIDDLE  ALT=\"x=-20%2F-4%2B4%2Asqrt%286%29%2F-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-20%2F-4-4%2Asqrt%286%29%2F-4 ALIGN=MIDDLE  ALT=\"x=-20%2F-4-4%2Asqrt%286%29%2F-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Simplify\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5-sqrt%286%29 ALIGN=MIDDLE  ALT=\"x=5-sqrt%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5%2Bsqrt%286%29 ALIGN=MIDDLE  ALT=\"x=5%2Bsqrt%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So our solutions are:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5-sqrt%286%29 ALIGN=MIDDLE  ALT=\"x=5-sqrt%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5%2Bsqrt%286%29 ALIGN=MIDDLE  ALT=\"x=5%2Bsqrt%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );