document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=817753>Question 817753</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Could someone explain to me how to solve:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%283%29%2F%28x%2B2%29%2B%281%29%2F%28x-2%29=%287%29%2F%28x%5E2-4%29+ ALIGN=MIDDLE  ALT=\"+%283%29%2F%28x%2B2%29%2B%281%29%2F%28x-2%29=%287%29%2F%28x%5E2-4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "I get to: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28%283%29%28x-2%29%2B%281%29%28x%2B2%29%29%2F%28x%2B2%29%28x-2%29=%287%29%2F%28x%5E2-4%29+ ALIGN=MIDDLE  ALT=\"+%28%283%29%28x-2%29%2B%281%29%28x%2B2%29%29%2F%28x%2B2%29%28x-2%29=%287%29%2F%28x%5E2-4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%284x-4%29%2F%28x%5E2-4%29+=+7%2F%28x%5E2-4%29+ ALIGN=MIDDLE  ALT=\"+%284x-4%29%2F%28x%5E2-4%29+=+7%2F%28x%5E2-4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "And: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%284x-4%29%28x%5E2-4%29+=+7%28x%5E2-4%29+ ALIGN=MIDDLE  ALT=\"+%284x-4%29%28x%5E2-4%29+=+7%28x%5E2-4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Expand: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4x%5E3-16x-4x%5E2%2B16+=+7x%5E2-28+ ALIGN=MIDDLE  ALT=\"+4x%5E3-16x-4x%5E2%2B16+=+7x%5E2-28+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Rearrange: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4x%5E3+-11x%5E2-16x%2B44+=+0+ ALIGN=MIDDLE  ALT=\"+4x%5E3+-11x%5E2-16x%2B44+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Now I either made a serious mistake somewhere or maybe I just don't know what to do next.<BR>\n" );
document.write( "Equation should have 2 answers<BR>\n" );
document.write( "Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #492172 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=492172\">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=+%284x-4%29%2F%28x%5E2-4%29+=+7%2F%28x%5E2-4%29+ ALIGN=MIDDLE  ALT=\"+%284x-4%29%2F%28x%5E2-4%29+=+7%2F%28x%5E2-4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "At this point, keeping in mind that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2 ALIGN=MIDDLE  ALT=\"x=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-2 ALIGN=MIDDLE  ALT=\"x=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > cannot be the final solutions, because they make denominators zero,<BR>\n" );
document.write( "you just solve<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x-4=7 ALIGN=MIDDLE  ALT=\"4x-4=7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x=11 ALIGN=MIDDLE  ALT=\"4x=11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=11%2F4 ALIGN=MIDDLE  ALT=\"x=11%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "NOTES:<BR>\n" );
document.write( "The denominators in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%284x-4%29%2F%28x%5E2-4%29+=+7%2F%28x%5E2-4%29+ ALIGN=MIDDLE  ALT=\"+%284x-4%29%2F%28x%5E2-4%29+=+7%2F%28x%5E2-4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "are the same on both sides of the equal sign,<BR>\n" );
document.write( "so the numerators have to be the same.<BR>\n" );
document.write( "You could say that you are multiplying both sides of the equation times <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-4 ALIGN=MIDDLE  ALT=\"x%5E2-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "to get an equation that is equivalent as long as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-4%3C%3E0 ALIGN=MIDDLE  ALT=\"x%5E2-4%3C%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "If you had found <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2 ALIGN=MIDDLE  ALT=\"x=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and/or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-2 ALIGN=MIDDLE  ALT=\"x=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > as solutions of the transformed equation,<BR>\n" );
document.write( "you would say it is/they are \"extraneous solution(s)\",<BR>\n" );
document.write( "solutions that were introduced by multiplying times <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-4 ALIGN=MIDDLE  ALT=\"x%5E2-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > that are not solutions of the original equation.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );