document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=195474>Question 195474</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The directions say for the pair of functions f and g, find all values of a for which f(a) =g(a)\r<BR>\n" );
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document.write( "f(x) = y/y^2+7y+10  +   y/y^2-4\r<BR>\n" );
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document.write( "g(x) = y/y^2+3y-10\r<BR>\n" );
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document.write( "my answer was y^2=0 and y=0 but I don't think that correct </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #146620 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=146620\">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( "Missed it by <b><i>that</i></b> much.\r<BR>\n" );
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document.write( "Simply set the two functions equal to each other and solve the resulting quadratic:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{y}{y^2 + 7y + 10}+\frac{y}{y^2 - 4} = \frac{y}{y^2 +3y -10}\">\r<BR>\n" );
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document.write( "Factor all three denominators:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{y}{(y + 2)(y + 5)}+\frac{y}{(y + 2)(y - 2)} = \frac{y}{(y - 2)(y + 5)}\">\r<BR>\n" );
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document.write( "Three different factors in all the denominators, so the LCD is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ (y + 2)(y - 2)(y + 5)\">\r<BR>\n" );
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document.write( "Apply the LCD:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{y(y - 2) + y(y + 5)}{(y + 2)(y - 2)(y + 5)} = \frac{y(y + 2)}{(y + 2)(y - 2)(y + 5)}\">\r<BR>\n" );
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document.write( "Multiply both sides by the LCD to eliminate the denominators:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y(y - 2) + y(y + 5) = y(y + 2)\">\r<BR>\n" );
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document.write( "Distribute to remove parentheses:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y^2 - 2y + y^2 + 5y = y^2 + 2y\">\r<BR>\n" );
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document.write( "Collect like terms on the left:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y^2 + y = 0\">\r<BR>\n" );
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document.write( "Factor:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y(y + 1) = 0\">\r<BR>\n" );
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document.write( "Use the Zero Product Rule:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y = 0\"> or\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y = -1\">\r<BR>\n" );
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document.write( "Verification of all elements of the solution set is left as an exercise for the student.\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" );
document.write( "</font> </SPAN>\n" );
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