document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1098557>Question 1098557</A>: <I><SPAN STYLE=\"word-break: break-all;\"> write down the reciprocal of:-\r<BR>\n" );
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document.write( "1/xy, 2f-v/fv </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #712967 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=712967\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "in general, the reciprocal of a is equal to 1/a and the reciprocal of a/b is equal to b/a.\r<BR>\n" );
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document.write( "in the expression of 1 / (xy), the reciprocal is equal to (xy) / 1, which is equal to (xy).\r<BR>\n" );
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document.write( "in the expression of (2f-v) / (fv), the reciprocal is equal to  (fv) / (2f-v).\r<BR>\n" );
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document.write( "you can confirm by assigning arbitrary values to the variables to see if the basic concept of a reciprocal being 1 divided by the expression holds true.\r<BR>\n" );
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document.write( "in the expression of 1 / (xy), if you let x = 2 and y = 3, the expression becomes 1 / 6.\r<BR>\n" );
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document.write( "the reciprocal should be 1 / (1/6) which is equal to 6.\r<BR>\n" );
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document.write( "x * y is the reciprocal and is equal to 2 * 3 which is equal to 6, so the concept of reciprocality holds.\r<BR>\n" );
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document.write( "in the expression of (2f-v) / (fv), if you let f = 2 and v = 3, then the expression becomes (2*2-3) / (2*3) which is equal to 1/6.\r<BR>\n" );
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document.write( "the reciprocal of 1/6 is equal to 6.\r<BR>\n" );
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document.write( "(fv) / (2f-v) is equal to (2*3) / (2*2-3) which is equal to 6/1 which is equal to 6.\r<BR>\n" );
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document.write( "the concept of reciprocality holds here as well.\r<BR>\n" );
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document.write( "the reciprocal of any expression is 1 divided by that expression.\r<BR>\n" );
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document.write( "the rest is just mathematical manipulation to get it to look like what you want.\r<BR>\n" );
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document.write( "for example, you can say that the reciprocal of (a/b) / (c/d) is equal to (c/d) / (a/b), but how did you get there?\r<BR>\n" );
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document.write( "the reciprocal of (a/b) / (c/d) is equal to 1 / ((a/b) / (c/d))\r<BR>\n" );
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document.write( "your numerator is 1 and your denominator is (a/b) / (c/d).\r<BR>\n" );
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document.write( "multiply both numerator and denominator by (c/d) and:\r<BR>\n" );
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document.write( "your numerator becomes 1 * (c/d) which is equal to (c/d).\r<BR>\n" );
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document.write( "your denominator becomes (a/b) / (c/d) * (c/d) which is equal to (a/b).\r<BR>\n" );
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document.write( "your expression becomes (c/d) / (a/b).\r<BR>\n" );
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document.write( "reciprocal of (a/b) / (c/d) is (c/d) / a/b), all derived from the fact that:\r<BR>\n" );
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document.write( "the reciprocal of (a/b) / (c/d) is equal to 1 divided by (a/b) / (c/d).\r<BR>\n" );
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document.write( "note that when you multiply the numerator of an expression and the denominator of an expression by the same amount, the value of the expression remains the same.\r<BR>\n" );
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document.write( "example:\r<BR>\n" );
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document.write( "3/6 * 5/5 = 15/30 which is the same as 3/6 which is the same as 1/2.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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