document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=140791>Question 140791</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Add or subtract the fractions then simplify using the Pythagorean identities and factoring to find the expression that completes the identity.\r<BR>\n" );
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document.write( "sinx/(cosx+1) + (cosx+1)/sin x\r<BR>\n" );
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document.write( "Please show me the steps.  Thank you!  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #102462 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=102462\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I can show you how to add the fractions, but since there is no equal sign anywhere, there is no \"identity\"\r<BR>\n" );
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document.write( "You add the fractions just like you would add any other fractions.  You find a common denominator, convert the numerators, and then sum the numerators.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sin%28x%29%2F%28cos%28x%29%2B1%29%29%28%28cos%28x%29%2B1%29%2Fsin%28x%29%29 ALIGN=MIDDLE  ALT=\"%28sin%28x%29%2F%28cos%28x%29%2B1%29%29%28%28cos%28x%29%2B1%29%2Fsin%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The two denominators have no factors in common, so the lowest common denominator is simply the product of the denominators, exactly like adding <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F5%2B1%2F7 ALIGN=MIDDLE  ALT=\"1%2F5%2B1%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" > where the LCD is just <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2A7=35 ALIGN=MIDDLE  ALT=\"5%2A7=35\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So your LCD is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28x%29%28cos%28x%29%2B1%29 ALIGN=MIDDLE  ALT=\"sin%28x%29%28cos%28x%29%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and your sum becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sin%5E2%28x%29%2B%28cos%28x%29%2B1%29%5E2%29%2F%28sin%28x%29%28cos%28x%29%2B1%29%29 ALIGN=MIDDLE  ALT=\"%28sin%5E2%28x%29%2B%28cos%28x%29%2B1%29%5E2%29%2F%28sin%28x%29%28cos%28x%29%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sin%5E2%28x%29+%2B+cos%5E2%28x%29%2B2cos%28x%29%2B1%29%2F%28sin%28x%29%28cos%28x%29%2B1%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "But we know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%5E2%28x%29%2Bcos%5E2%28x%29=1 ALIGN=MIDDLE  ALT=\"sin%5E2%28x%29%2Bcos%5E2%28x%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > so:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2B2cos%28x%29%2B1%29%2F%28sin%28x%29%28cos%28x%29%2B1%29%29 ALIGN=MIDDLE  ALT=\"%281%2B2cos%28x%29%2B1%29%2F%28sin%28x%29%28cos%28x%29%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282cos%28x%29%2B2%29%2F%28sin%28x%29%28cos%28x%29%2B1%29%29 ALIGN=MIDDLE  ALT=\"%282cos%28x%29%2B2%29%2F%28sin%28x%29%28cos%28x%29%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cartoon%28%282%28cos%28x%29%2B1%29%29%2F%28sin%28x%29%28cos%28x%29%2B1%29%29%2C%282%2Across%28%28cos%28x%29%2B1%29%29%29%2F%28sin%28x%29cross%28%28cos%28x%29%2B1%29%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Fsin%28x%29 ALIGN=MIDDLE  ALT=\"2%2Fsin%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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