document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=6601>Question 6601</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please help me with this:\r<BR>\n" );
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document.write( "For a value of K, the expression x+k/x^2+kx-15 is undefined when x=5 and x=-3. Find the value of K </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #3593 by </B><A HREF=/tutors/aboutme.mpl?userid=prince_abubu><B>prince_abubu(198)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=prince_abubu><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=3593\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The trick here lies in the denominator. Hang on for the ride. This is a bit tricky.\r<BR>\n" );
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document.write( "I take it that you know that 5 and -3 will make the expression fail because those two values will force the denominator to be equal to 0.\r<BR>\n" );
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document.write( "They already gave you the fact that the denominator is quadratic (because of the x^2 term), and that quadratic expression can be factored in (x + _)(x + _) form (reverse-FOILING). We now need to set that denominator equal to zero to find which values of x make that denominator zero. In other words, we are looking for illegal values of x. So far, we have the equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x+%2B+_%29%28x+%2B+_%29+=+0+ ALIGN=MIDDLE  ALT=\"+%28x+%2B+_%29%28x+%2B+_%29+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "But what values do you put in place of the blanks? Ah! They gave you the x-values already - the 5 and the -3. So, substitute the 5 and the -3 for each of the x's, NOT the blanks. Now we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%285+%2B+_%29%28-3+%2B+_%29+=+0+ ALIGN=MIDDLE  ALT=\"+%285+%2B+_%29%28-3+%2B+_%29+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Remember that 0 times anything equals zero. So we'll pick at the first set of parentheses and set it equal to zero:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%285+%2B+_%29+=+0+ ALIGN=MIDDLE  ALT=\"+%285+%2B+_%29+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > You'll see that _ = -5\r<BR>\n" );
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document.write( "Let's take the second set of parentheses and set it equal to zero.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-3+%2B+_%29+=+0+ ALIGN=MIDDLE  ALT=\"+%28-3+%2B+_%29+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > You'll see that _ = 3\r<BR>\n" );
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document.write( "Now rewrite the equation with the x's and place the two values you found for the blanks:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x+-+5%29%28x+%2B+3%29+=+0+ ALIGN=MIDDLE  ALT=\"+%28x+-+5%29%28x+%2B+3%29+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "NOTE: We could've just agreed to write write the quadratic in (x + _)(x + _) form and just plug in the undefined values given and change the signs. So we could've straight up said (x - 5)(x + 3) = 0 (plug in the numbers but reverse the signs just because it works out that way), but I just wanted to show you why and how it works that way.\r<BR>\n" );
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document.write( "Now, do FOIL on the (x - 5)(x + 3). This turns out to be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2+-+2x+-+15+ ALIGN=MIDDLE  ALT=\"+x%5E2+-+2x+-+15+\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Now put that head to head with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2+%2B+kx+-+15+ ALIGN=MIDDLE  ALT=\"+x%5E2+%2B+kx+-+15+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and you'll see that k = -2. \r<BR>\n" );
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document.write( "WARNING. Don't let the \"+ k\" vs. the \"- 2\" fool you into believing that there is no way to work out this problem. When you see \"+ k\" or \"+ any variable\", it just means that k can be any number. If k turned out to be negative, like in this case, it really is \"+ -2\" which turns out to be \"- 2\".\r<BR>\n" );
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