document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=84530>Question 84530</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/061849281X/algebrahomeworkh>College Agebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Find the real values of x such that f(x)=0 (directions).\r<BR>\n" );
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document.write( "f(x)=3/x-1 + 4/x-2 - - I don't even know where to begin on this problem. the answer they gave is 10/7 and I'm really confused on that.... </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #60873 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=60873\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Just set f(x) equal to zero. When you do that the given equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F%28x-1%29+%2B+4%2F%28x-2%29+=+0 ALIGN=MIDDLE  ALT=\"3%2F%28x-1%29+%2B+4%2F%28x-2%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now get rid of the denominators by multiplying all terms (on both sides) of this equation <BR>\n" );
document.write( "by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29%2A%28x-2%29 ALIGN=MIDDLE  ALT=\"%28x-1%29%2A%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. When you do that multiplication you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2A%28x-1%29%2A%28x-2%29%29%2F%28x-1%29+%2B+%284%2A%28x-1%29%2A%28x-2%29%29%2F%28x-2%29+=+0 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Note that the right side of the equation remains zero because 0 times anything is still <BR>\n" );
document.write( "zero. Note also that you can now cancel the terms in the denominator with the same term <BR>\n" );
document.write( "in the numerator. The result is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2A%28cross%28x-1%29%29%2A%28x-2%29%29%2F%28cross%28x-1%29%29+%2B+%284%2A%28x-1%29%2A%28cross%28x-2%29%29%29%2F%28cross%28x-2%29%29+=+0 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "And the equation reduces to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A%28x-2%29+%2B+4%2A%28x-1%29+=+0 ALIGN=MIDDLE  ALT=\"3%2A%28x-2%29+%2B+4%2A%28x-1%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Multiply out the terms to get:<BR>\n" );
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document.write( "3x - 6 + 4x - 4 = 0<BR>\n" );
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document.write( "Combine the x terms and the equation becomes:<BR>\n" );
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document.write( "7x – 6 – 4 = 0<BR>\n" );
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document.write( "Combine the -6 with the -4 and the equation further becomes:<BR>\n" );
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document.write( "7x – 10 = 0<BR>\n" );
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document.write( "Eliminate the -10 from the left side by adding +10 to both sides. This makes the equation:<BR>\n" );
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document.write( "7x = 10<BR>\n" );
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document.write( "Finally, solve for x by dividing both sides of the equation by 7 which is the multiplier <BR>\n" );
document.write( "of the x term.  The division results in the answer:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=10%2F7 ALIGN=MIDDLE  ALT=\"x=10%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Hope this helps you understand the problem.<BR>\n" );
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