document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=95623>Question 95623</A>: <I><SPAN STYLE=\"word-break: break-all;\"> These do not come from a textbook; only a worksheet.  Please help!  Thanks.\r<BR>\n" );
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document.write( "1.  Solve the equation.<BR>\n" );
document.write( "    t/t-2 = 7/t-2 + 2\r<BR>\n" );
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document.write( "2.  Solve for x.<BR>\n" );
document.write( "    x + 5 + x/x-5 = 5/x-5 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #69863 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=69863\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. Solve the equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%2F%28t-2%29 ALIGN=MIDDLE  ALT=\"t%2F%28t-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2F%28t-2%29 ALIGN=MIDDLE  ALT=\"7%2F%28t-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + 2<BR>\n" );
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document.write( "WE can get rid of the denominators by multiplying equation by(t-2) like this:<BR>\n" );
document.write( "(t-2)<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%2F%28t-2%29 ALIGN=MIDDLE  ALT=\"t%2F%28t-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = (t-2)<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2F%28t-2%29 ALIGN=MIDDLE  ALT=\"7%2F%28t-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + 2(t-2)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Cancel out the denominators leaving you with:<BR>\n" );
document.write( " t = 7 + 2(t-2)<BR>\n" );
document.write( " t = 7 + 2t - 4: multiplied what's inside the brackets<BR>\n" );
document.write( " t = 2t + 3<BR>\n" );
document.write( " t - 2t = 3; subtracted 2t from both sides<BR>\n" );
document.write( " -t = 3<BR>\n" );
document.write( "  t = -3; multiplied equation by -1, we always want the variable to be positive<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Check solution in original equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-3%29%2F%28-3-2%29 ALIGN=MIDDLE  ALT=\"%28-3%29%2F%28-3-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2F%28-3-2%29 ALIGN=MIDDLE  ALT=\"7%2F%28-3-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + 2<BR>\n" );
document.write( ":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-3%29%2F%28-5%29 ALIGN=MIDDLE  ALT=\"%28-3%29%2F%28-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2F%28-5%29 ALIGN=MIDDLE  ALT=\"7%2F%28-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2F5 ALIGN=MIDDLE  ALT=\"10%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which is:<BR>\n" );
document.write( "+<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F5 ALIGN=MIDDLE  ALT=\"3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7%2F5 ALIGN=MIDDLE  ALT=\"-7%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2F5 ALIGN=MIDDLE  ALT=\"10%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "2. Solve for x.<BR>\n" );
document.write( "x + 5 + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F%28x-5%29 ALIGN=MIDDLE  ALT=\"x%2F%28x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F%28x-5%29 ALIGN=MIDDLE  ALT=\"5%2F%28x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply equation by (x-5) to get rid of the denominators<BR>\n" );
document.write( "x(x-5) + 5(x-5) + (x-5)<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F%28x-5%29 ALIGN=MIDDLE  ALT=\"x%2F%28x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = (x-5)<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F%28x-5%29 ALIGN=MIDDLE  ALT=\"5%2F%28x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "x^2 - 5x + 5x - 25 + x = 5<BR>\n" );
document.write( "x^2 + x - 25 - 5 = 0<BR>\n" );
document.write( "x^2 + x - 30 = 0; a quadratic equation:<BR>\n" );
document.write( "Factors to:<BR>\n" );
document.write( "(x+6)(x-5) = 0<BR>\n" );
document.write( "x = -6<BR>\n" );
document.write( "and<BR>\n" );
document.write( "x = +5<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Check solution using x = -6 in original equation:<BR>\n" );
document.write( "-6 + 5 + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-6%29%2F%28-6-5%29 ALIGN=MIDDLE  ALT=\"%28-6%29%2F%28-6-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F%28-6-5%29 ALIGN=MIDDLE  ALT=\"5%2F%28-6-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "-1 + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-6%29%2F%28-11%29 ALIGN=MIDDLE  ALT=\"%28-6%29%2F%28-11%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F%28-11%29 ALIGN=MIDDLE  ALT=\"5%2F%28-11%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-11%2F11 ALIGN=MIDDLE  ALT=\"-11%2F11\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286%29%2F%2811%29 ALIGN=MIDDLE  ALT=\"%286%29%2F%2811%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5%2F%2811%29 ALIGN=MIDDLE  ALT=\"-5%2F%2811%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "I better point out to you that x=+5 is not a solution, it puts a 0 as the<BR>\n" );
document.write( "denominator in the original equation, a big no-no in algebra<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );