document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=160217>Question 160217</A>: <I><SPAN STYLE=\"word-break: break-all;\"> -3 over 4 S - 3 = 1 over 3 S + 1 over 4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #118182 by </B><A HREF=/tutors/aboutme.mpl?userid=midwood_trail><B>midwood_trail(310)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=midwood_trail><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=118182\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (-3/4s) - (3/1) = 1/(3s) + 1/4\r<BR>\n" );
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document.write( "Here is the correct set up equation:<BR>\n" );
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document.write( "(-3/4S) - 3/1 = (1/3S) + 1/4<BR>\n" );
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document.write( "I needed to put parentheses for easy reading.  Any number or letter by itself = that number or letter over 1.<BR>\n" );
document.write( "So, -3 is really -3/1 but we never write this way except in math courses.<BR>\n" );
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document.write( "Back to your question.<BR>\n" );
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document.write( "I will solve for S and let you prove it.<BR>\n" );
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document.write( "(-3 - 4(4S))/4S = 7/12S<BR>\n" );
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document.write( "(-3 -12S)/4S = 7/12S<BR>\n" );
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document.write( "We now cross-multiply.<BR>\n" );
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document.write( "4S times 7 = (12S) times the quantity (-3 - 12S)<BR>\n" );
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document.write( "28S = -36S - 144S^2<BR>\n" );
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document.write( "Set everything to zero.<BR>\n" );
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document.write( "144S^2 + 36S - 28S = 0<BR>\n" );
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document.write( "144S^2 + 8S = 0<BR>\n" );
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document.write( "Factor out 8S.<BR>\n" );
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document.write( "8S(18S + 1) = 0<BR>\n" );
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document.write( "We now have two factors:<BR>\n" );
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document.write( "8S and the quantity (18S + 1)<BR>\n" );
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document.write( "Set each factor to zero and solve for S.<BR>\n" );
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document.write( "8S = 0<BR>\n" );
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document.write( "S = 0/8<BR>\n" );
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document.write( "S = 0<BR>\n" );
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document.write( "Next factor:<BR>\n" );
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document.write( "18S + 1 = 0<BR>\n" );
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document.write( "18S = -1<BR>\n" );
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document.write( "S = -1/18<BR>\n" );
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document.write( "We have two answers for S, but which one is the right one?<BR>\n" );
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document.write( "To find out, replace S in your original fractional equation given with 0 and simplify and then replace S again <BR>\n" );
document.write( "with -1/18 and simplify.<BR>\n" );
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document.write( "Whichever value for S gives you the same answer on both sides of the equation, that will be your correct value for S.<BR>\n" );
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document.write( "Don't be surprised if BOTH S = 0 and S = -1/18 are correct.<BR>\n" );
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document.write( "I will let you plug and chug.<BR>\n" );
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document.write( "If you cannot do this, write back but please try on your own first.  I did most of the work in your place.<BR>\n" );
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document.write( "midwood_trail\r<BR>\n" );
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