document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=457927>Question 457927</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Prove that if 0 < a < 1 and 0 < b < 1, then 0 < a + b - ab < 1. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #314119 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=314119\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Take note that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?a + b - ab = -(a-1)(b-1)+1\"> (a factoring technique I've heard as \"Simon's Favorite Factoring Trick\" on a math website but I don't know if it really has a name). The numbers a-1 and b-1 range between -1 and 0, so\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 0 < (a-1)(b-1) < 1\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE -1 < -(a-1)(b-1) < 0\"> Add 1 to both sides:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 0 < -(a-1)(b-1) + 1 < 1\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 0 < a + b - ab < 1\"> and we are done. </SPAN>\n" );
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