document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=198040>Question 198040</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need to find the sum or difference with unlike denominators\r<BR>\n" );
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document.write( "1.  (y+2)/ (y^2+5y+6) + (2-y)/(y^2+y-6)<BR>\n" );
document.write( "I did (y+2)/(y+3)(y+2) + (2-y) /(y+3)(y-2)<BR>\n" );
document.write( "I crossed out the y+2 and the y-2 and then left with 1/(y+3)(y+3) = 1/2y+6\r<BR>\n" );
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document.write( "2.  (1)/(X) + (7)/(3x)<BR>\n" );
document.write( "I times 1/x by 3/3 and got 1/x.3/3 + 7/3x.1/1 = 10/6x^2\r<BR>\n" );
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document.write( "Please help....I'm very confused<BR>\n" );
document.write( "Thanks,<BR>\n" );
document.write( "JC </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #148514 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=148514\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "Once you have determined a common denominator, adding fractions is simply the sum of the numerators over that common denominator.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{y + 2}{y^2 + 5y  + 6} + \frac{2 - y}{y^2 + y - 6}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{y + 2}{(y + 3)(y + 2)} + \frac{2 - y}{(y + 3)(y - 2)}\">\r<BR>\n" );
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document.write( "So far, so good.  But realize that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 2 - y = - (y - 2)\">, so:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{1}{y + 3} + \frac{-1}{y + 3}\">\r<BR>\n" );
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document.write( "Now just add the numerators -- <b><i>do not</i></b> add the denominators\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{1 - 1}{y + 3}\ =\ 0\">\r<BR>\n" );
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document.write( "===============================================\r<BR>\n" );
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document.write( "You started with the correct strategy, i.e. you multiplied the left hand fraction by 3 over 3, but then you again added the denominators when you were adding the fractions.  Your result should have been:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{10}{3x}\">\r<BR>\n" );
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document.write( "And, by the way, you also made an error when you added the denominators:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 3x + 3x \neq 6x^2\"> rather <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 3x + 3x = 6x\">\r<BR>\n" );
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document.write( "Remember adding fractions in elementary school:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{1}{4} + \frac{1}{4} = \frac{2}{4} = \frac{1}{2}\">\r<BR>\n" );
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document.write( "<b><i>not</i></b>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{1}{4} + \frac{1}{4} \neq \frac{2}{8} = \frac{1}{4}\">\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
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