document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=707909>Question 707909</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Change the rational equation to quadratic form and solve it by the most efficient method. (Enter your answers as a comma-separated list.)<BR>\n" );
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document.write( "x(2x + 1)/ x-4= 36/x-4<BR>\n" );
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document.write( "I keep getting the answers 4 and -9/2 but its not right. I have tried multiplying both fractions by x-4 to get rid of them. then from there i have done quadratic formula and completing the square and i still get the same answers  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #435914 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=435914\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If the problem is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%282x%2B1%29%29%2F%28x-4%29+=+36%2F%28x-4%29 ALIGN=MIDDLE  ALT=\"%28x%282x%2B1%29%29%2F%28x-4%29+=+36%2F%28x-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then you can multiply both sides by x-4 to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%282x%2B1%29+=+36 ALIGN=MIDDLE  ALT=\"x%282x%2B1%29+=+36\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "If you solve that for x, you will get 4, -9/2 ... BUT...these are the solutions to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%282x%2B1%29+=+36 ALIGN=MIDDLE  ALT=\"x%282x%2B1%29+=+36\"   DISABLED_style= \"max-width:90%; height:auto;\" > and NOT the original equation.\r<BR>\n" );
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document.write( "This is why you must check any and all possible answers you get in the original equation.\r<BR>\n" );
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document.write( "Notice that if x = 4, then x - 4 is equal to zero. But x-4 is a denominator and if that is zero, then you have a division by zero error. To avoid this division by zero error, you make the restriction that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C%3E4 ALIGN=MIDDLE  ALT=\"x%3C%3E4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So x = 4 is NOT a solution\r<BR>\n" );
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document.write( "This just leaves the only solution to be -9/2 </SPAN>\n" );
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