document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=150442>Question 150442</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The following appears to prove that any two numbers are equal. Obviously it is wrong; can you spot the flaw? \r<BR>\n" );
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document.write( "Let a and b be any two different numbers. Define x as the difference between them:\r<BR>\n" );
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document.write( "x = b - a<BR>\n" );
document.write( "Multiply both sides of the equation by (b-a):<BR>\n" );
document.write( "x(b – a) = (b – a)(b – a)<BR>\n" );
document.write( "bx – ax = b^2 – 2ab + a^2<BR>\n" );
document.write( "Add –bx+ab-a^2 to both sides and simplify:<BR>\n" );
document.write( "bx – ax – bx + ab – a^2 = b^2 – 2ab + a^2 – bx + ab – a^2<BR>\n" );
document.write( "bx – bx – ax + ab – a^2 = –bx + b^2 – 2ab + ab + a^2 – a^2<BR>\n" );
document.write( "–ax + ab – a^2 = –bx + b^2 – ab<BR>\n" );
document.write( "Both sides of this equation have a common factor:<BR>\n" );
document.write( "a(–x + b – a) = b(–x + b – a)<BR>\n" );
document.write( "Divide both sides by (-x+b-a):<BR>\n" );
document.write( "a(–x + b – a)/-x + b-a = b(–x + b – a)/ -x + b - a<BR>\n" );
document.write( "a = b   <BR>\n" );
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document.write( "What was my mistake?\r<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 #110388 by </B><A HREF=/tutors/aboutme.mpl?userid=vleith><B>vleith(2983)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=vleith><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=110388\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You said \"Divide both sides by (-x+b-a)\"\r<BR>\n" );
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document.write( "But what is x?<BR>\n" );
document.write( "x = b-a\r<BR>\n" );
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document.write( "So what is (-x + b -a)?<BR>\n" );
document.write( "(-b + a + b - a) = 0\r<BR>\n" );
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document.write( "You can make 'anything' happen if you allow division by zero. Which is why division by zero is undefined.\r<BR>\n" );
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