document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209876>Question 1209876</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the largest value of x where the plots of<BR>\n" );
document.write( "f(x) = - \frac{2x + 5}{x + 3} and g(x) = \frac{12}{x - 1}<BR>\n" );
document.write( "intersect.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #851969 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52810)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=851969\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "Polynomials-and-rational-expressions/1209876: Find the largest value of x where the plots of<BR>\n" );
document.write( "f(x) = - \frac{2x + 5}{x + 3} and g(x) = \frac{12}{x - 1}<BR>\n" );
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document.write( "Be aware !\r<BR>\n" );
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document.write( "The answer in the post by @CPhill is incorrect.\r<BR>\n" );
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document.write( "He made an arithmetic error while calculated the discriminant of the quadratic equation.\r<BR>\n" );
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document.write( "The discriminant is NEGATIVE, which means that the quadratic equation does not have real solutions.\r<BR>\n" );
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document.write( "The answer is that the plots of these given functions do not intersect in real domain.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Regarding the post by @CPhill . . . \r<BR>\n" );
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document.write( "Keep in mind that @CPhill is a pseudonym for the Google artificial intelligence.\r<BR>\n" );
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document.write( "The artificial intelligence is like a baby now. It is in the experimental stage <BR>\n" );
document.write( "of development and can make mistakes and produce nonsense without any embarrassment.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;It has no feeling of shame - it is shameless.\r<BR>\n" );
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document.write( "This time, again, &nbsp;it made an error.\r<BR>\n" );
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document.write( "Although the @CPhill' solutions are copy-paste &nbsp;Google &nbsp;AI solutions, &nbsp;there is one essential difference.\r<BR>\n" );
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document.write( "Every time, &nbsp;Google &nbsp;AI &nbsp;makes a note at the end of its solutions that &nbsp;Google &nbsp;AI &nbsp;is experimental<BR>\n" );
document.write( "and can make errors/mistakes.\r<BR>\n" );
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document.write( "All @CPhill' solutions are copy-paste of &nbsp;Google &nbsp;AI &nbsp;solutions, with one difference:<BR>\n" );
document.write( "@PChill never makes this notice and never says that his solutions are copy-past that of Google.<BR>\n" );
document.write( "So, &nbsp;he &nbsp;NEVER &nbsp;SAYS &nbsp;TRUTH.\r<BR>\n" );
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document.write( "Every time, &nbsp;@CPhill embarrassed to tell the truth.\r<BR>\n" );
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document.write( "But I am not embarrassing to tell the truth, &nbsp;as it is my duty at this forum.\r<BR>\n" );
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document.write( "And the last my comment.\r<BR>\n" );
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document.write( "When you obtain such posts from @CPhill, &nbsp;remember, &nbsp;that &nbsp;NOBODY &nbsp;is responsible for their correctness, <BR>\n" );
document.write( "until the specialists and experts will check and confirm their correctness.\r<BR>\n" );
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document.write( "Without it, &nbsp;their reliability is &nbsp;ZERO and their creadability is &nbsp;ZERO, &nbsp;too.\r<BR>\n" );
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document.write( "In his post, @greenestamps presented a result, &nbsp;different from mine.\r<BR>\n" );
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document.write( "It is because, &nbsp;by mistake, &nbsp;he solved &nbsp;DIFFERENT &nbsp;equation than it is given in the original post.\r<BR>\n" );
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document.write( "In the original post, &nbsp;the equations/functions were \r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;f(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%282x+%2B+5%29%2F%28x+%2B+3%29 ALIGN=MIDDLE  ALT=\"-%282x+%2B+5%29%2F%28x+%2B+3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > &nbsp;&nbsp;and &nbsp;&nbsp;g(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2F%28x+-+1%29 ALIGN=MIDDLE  ALT=\"12%2F%28x+-+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "In his post, &nbsp;@greenestamps mistakenly used functions\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;f(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x+%2B+5%29%2F%28x+%2B+3%29 ALIGN=MIDDLE  ALT=\"%282x+%2B+5%29%2F%28x+%2B+3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > &nbsp;&nbsp;and &nbsp;&nbsp;g(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2F%28x+-+1%29 ALIGN=MIDDLE  ALT=\"12%2F%28x+-+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Notice that his function &nbsp;f(x) &nbsp;has the opposite sign, &nbsp;comparing with the given function &nbsp;f(x).\r<BR>\n" );
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document.write( "Therefore, &nbsp;it is no wonder that he came to different answer, &nbsp;comparing with mine.\r<BR>\n" );
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document.write( "Thus my conclusion remains unchangeable:\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;the solution and the answer in the post by @CPhill both are incorrect.\r<BR>\n" );
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document.write( "In the post by &nbsp;Edwin, &nbsp;he made the same error, &nbsp;which @greenestamps made in his post.\r<BR>\n" );
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document.write( "Edwin plotted function  &nbsp;&nbsp;f(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%2B5%29%2F%28x%2B3%29 ALIGN=MIDDLE  ALT=\"%282x%2B5%29%2F%28x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,  &nbsp;&nbsp;while in the original problem the given function is with the opposite sign &nbsp;&nbsp;f(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%282x%2B5%29%2F%28x%2B3%29 ALIGN=MIDDLE  ALT=\"-%282x%2B5%29%2F%28x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "So, &nbsp;it is not wonder that using wrong function, &nbsp;Edwin got wrong answer.\r<BR>\n" );
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document.write( "For your convenience, I prepared the plot of the given functions. &nbsp;&nbsp;It is shown under this link\r<BR>\n" );
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document.write( "<A  rel=nofollow HREF=https://www.desmos.com/calculator/dog5dqdqlc>https://www.desmos.com/calculator/dog5dqdqlc</A> \r<BR>\n" );
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document.write( "https://www.desmos.com/calculator/dog5dqdqlc\r<BR>\n" );
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document.write( "In addition to my algebraic explanations in my post above, &nbsp;this plot clearly shows visually <BR>\n" );
document.write( "that there no any intersection/intersections between the plots of the given functions.\r<BR>\n" );
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