document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=116890>Question 116890</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve.\r<BR>\n" );
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document.write( "The combined resistance of two resistors r1 and r2 in a parallel circuit is given by the formula rt=   1 OVER 1/r1 + 1/r2. Simplify the formula. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #85002 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=85002\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5Bt%5D+=+1%2F%281%2Fr%5B1%5D+%2B+1%2Fr%5B2%5D%29 ALIGN=MIDDLE  ALT=\"r%5Bt%5D+=+1%2F%281%2Fr%5B1%5D+%2B+1%2Fr%5B2%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This is not the way this formula is usually written, but it is correct.<BR>\n" );
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document.write( "You can simplify this by multiplying the right side by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28r%5B1%5D%2Ar%5B2%5D%29%2F%28r%5B1%5D%2Ar%5B2%5D%29 ALIGN=MIDDLE  ALT=\"%28r%5B1%5D%2Ar%5B2%5D%29%2F%28r%5B1%5D%2Ar%5B2%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Since the numerator of this multiplier is equal to the denominator, this is the same as<BR>\n" );
document.write( "multiplying the right side by 1. This means that this multiplication doesn't change the<BR>\n" );
document.write( "value of the right side.<BR>\n" );
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document.write( "The multiplication leads to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5Bt%5D+=+%281%2F%281%2Fr%5B1%5D+%2B+1%2Fr%5B2%5D%29%29%2A%28%28r%5B1%5D%2Ar%5B2%5D%29%2F%28r%5B1%5D%2Ar%5B2%5D%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "A little difficult to see, maybe, but the very top \"1\" gets multiplied by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5B1%5D%2Ar%5B2%5D ALIGN=MIDDLE  ALT=\"r%5B1%5D%2Ar%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > and in<BR>\n" );
document.write( "the denominator the numerators of the two fractions (both numerators are \"1\") also get multiplied<BR>\n" );
document.write( "by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5B1%5D%2Ar%5B2%5D ALIGN=MIDDLE  ALT=\"r%5B1%5D%2Ar%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This changes the equation to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5Bt%5D+=+%28%281%2Ar%5B1%5D%2Ar%5B2%5D%29%2F%28%281%2Ar%5B1%5D%2Ar%5B2%5D%29%2Fr%5B1%5D+%2B+%281%2Ar%5B1%5D%2Ar%5B2%5D%29%2Fr%5B2%5D%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "In this, in the three places where a \"1\" is a multiplier, you can simplify the work by just <BR>\n" );
document.write( "erasing the \"1\". This simplifies the equation to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5Bt%5D+=+%28%28r%5B1%5D%2Ar%5B2%5D%29%2F%28%28r%5B1%5D%2Ar%5B2%5D%29%2Fr%5B1%5D+%2B+%28r%5B1%5D%2Ar%5B2%5D%29%2Fr%5B2%5D%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Then in the fractions in the denominator you can cancel the denominator of the fraction with<BR>\n" );
document.write( "the corresponding term in the numerator of the fraction as follows:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5Bt%5D+=+%28%28r%5B1%5D%2Ar%5B2%5D%29%2F%28%28cross%28r%5B1%5D%29%2Ar%5B2%5D%29%2Fcross%28r%5B1%5D%29+%2B+%28r%5B1%5D%2Across%28r%5B2%5D%29%29%2Fcross%28r%5B2%5D%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Note that the cancellations shown reduce the equation to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5Bt%5D+=+r%5B1%5D%2Ar%5B2%5D%2F%28r%5B2%5D+%2B+r%5B1%5D%29 ALIGN=MIDDLE  ALT=\"r%5Bt%5D+=+r%5B1%5D%2Ar%5B2%5D%2F%28r%5B2%5D+%2B+r%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "or by simply reversing the order of the terms in the denominator, which changes nothing, you <BR>\n" );
document.write( "get the more familiar form:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5Bt%5D+=+r%5B1%5D%2Ar%5B2%5D%2F%28r%5B1%5D+%2B+r%5B2%5D%29 ALIGN=MIDDLE  ALT=\"r%5Bt%5D+=+r%5B1%5D%2Ar%5B2%5D%2F%28r%5B1%5D+%2B+r%5B2%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This is the answer to the problem. It shows that two resistors connected in parallel can<BR>\n" );
document.write( "be replaced by a single resistor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5Bt%5D ALIGN=MIDDLE  ALT=\"r%5Bt%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > whose value is equal to the product of the two<BR>\n" );
document.write( "resistors divided by the sum of the two resistors. <BR>\n" );
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document.write( "Regarding my comment above, this problem does not list the formula for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5Bt%5D ALIGN=MIDDLE  ALT=\"r%5Bt%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > the way that it<BR>\n" );
document.write( "is usually written. The way it is usually given is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fr%5Bt%5D+=+1%2Fr%5B1%5D+%2B+1%2Fr%5B2%5D ALIGN=MIDDLE  ALT=\"1%2Fr%5Bt%5D+=+1%2Fr%5B1%5D+%2B+1%2Fr%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "If you solve this equation for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5Bt%5D ALIGN=MIDDLE  ALT=\"r%5Bt%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > you will get the same answer that we got for this problem ...<BR>\n" );
document.write( "namely you will again get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5Bt%5D+=+r%5B1%5D%2Ar%5B2%5D%2F%28r%5B1%5D+%2B+r%5B2%5D%29 ALIGN=MIDDLE  ALT=\"r%5Bt%5D+=+r%5B1%5D%2Ar%5B2%5D%2F%28r%5B1%5D+%2B+r%5B2%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Hope this helps you to understand the problem and how to solve it.<BR>\n" );
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