document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=535600>Question 535600</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a number is added to five time its reciprocal is -6. Find the number. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #351963 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=351963\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> As you described it, the problem you are trying to solve is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+5%2Fx+=+-6 ALIGN=MIDDLE  ALT=\"x+%2B+5%2Fx+=+-6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Get rid of the denominator by multiplying both sides of the equation (all terms) by x and you have:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2Ax%29+%2B+x%2A%285%2Fx%29+=+-6x ALIGN=MIDDLE  ALT=\"%28x%2Ax%29+%2B+x%2A%285%2Fx%29+=+-6x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Note that the first term on the left side becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "Also note that in the second term on the left side, you can cancel the multiplier x with the denominator x. After these two actions the equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+%28cross%28x%29%2A5%29%2Fcross%28x%29+=+-6x ALIGN=MIDDLE  ALT=\"x%5E2+%2B+%28cross%28x%29%2A5%29%2Fcross%28x%29+=+-6x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "which simplifies to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+5+=+-6x ALIGN=MIDDLE  ALT=\"x%5E2+%2B+5+=+-6x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Get rid of the -6x on the right side by adding +6x to both sides to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+6x+%2B+5+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+6x+%2B+5+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This quadratic equation can be factored as shown below:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+%2B+5%29%2A%28x+%2B+1%29+=+0 ALIGN=MIDDLE  ALT=\"%28x+%2B+5%29%2A%28x+%2B+1%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Note that this equation will be true if either of the factors is equal to zero. If either factor is equal to zero the left side will have a multiplication by zero and will, therefore, equal the zero on the right side. <BR>\n" );
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document.write( "So we can solve this equation by finding what numbers will make the two factors equal to zero. Do this by setting each factor (one at a time) equal to zero to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+5+=+0 ALIGN=MIDDLE  ALT=\"x+%2B+5+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is solved by subtracting 5 from both sides to get x = -5<BR>\n" );
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document.write( "and<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+1+=+0 ALIGN=MIDDLE  ALT=\"x+%2B+1+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is solved by subtracting 1 from both sides to get x = -1<BR>\n" );
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document.write( "Your problem has two correct answers. They are x = -5 and x = -1.<BR>\n" );
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document.write( "You can check these answers by returning to the original problem and substituting these values one at a time for x. <BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+5%2Fx+=+-6 ALIGN=MIDDLE  ALT=\"x+%2B+5%2Fx+=+-6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "set x = -5 and you have:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5+%2B+5%2F-5+=+-6 ALIGN=MIDDLE  ALT=\"-5+%2B+5%2F-5+=+-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > and this simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5+-1+=+-6 ALIGN=MIDDLE  ALT=\"-5+-1+=+-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is true.<BR>\n" );
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document.write( "Then set x = -1 and you have:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1+%2B+5%2F-1+=+-6 ALIGN=MIDDLE  ALT=\"-1+%2B+5%2F-1+=+-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > and this simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1+-5+=+-6 ALIGN=MIDDLE  ALT=\"-1+-5+=+-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is also true.<BR>\n" );
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document.write( "Both answers are OK because they make the original problem true.<BR>\n" );
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document.write( "Hope this helps you to understand the problem.<BR>\n" );
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