document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=107637>Question 107637</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find all the values of x satisfying the given conditions<BR>\n" );
document.write( "     1      2      -4<BR>\n" );
document.write( "y1= --- , ----, ---------, and y1+y2=y3<BR>\n" );
document.write( "    x+7    x+3  x^2+10+21\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #78402 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=78402\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Your problem as written doesn't make sense, but I'm going to make an assumption that does and go with that.  What I think you meant was:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y1=1%2F%28x%2B7%29 ALIGN=MIDDLE  ALT=\"y1=1%2F%28x%2B7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y2=2%2F%28x%2B3%29 ALIGN=MIDDLE  ALT=\"y2=2%2F%28x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y3=%28-4%29%2F%28x%5E2%2B10x%2B21%29 ALIGN=MIDDLE  ALT=\"y3=%28-4%29%2F%28x%5E2%2B10x%2B21%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y1%2By2=y3 ALIGN=MIDDLE  ALT=\"y1%2By2=y3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "That means we can say:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F%28x%2B7%29%29%2B%282%2F%28x%2B3%29%29=%28-4%29%2F%28x%5E2%2B10x%2B21%29 ALIGN=MIDDLE  ALT=\"%281%2F%28x%2B7%29%29%2B%282%2F%28x%2B3%29%29=%28-4%29%2F%28x%5E2%2B10x%2B21%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "To add the two terms on the left side, we need a Lowest Common Denominator, given by:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B7%29%28x%2B3%29=x%5E2%2B10x%2B21 ALIGN=MIDDLE  ALT=\"%28x%2B7%29%28x%2B3%29=x%5E2%2B10x%2B21\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now we have:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%2B3%29%2F%28x%5E2%2B10x%2B21%29%29%2B%282%28x%2B7%29%2F%28x%5E2%2B10x%2B21%29%29=%28-4%29%2F%28x%5E2%2B10x%2B21%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Simplify:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x%2B17%29%2F%28x%5E2%2B10x%2B21%29=%28-4%29%2F%28x%5E2%2B10x%2B21%29 ALIGN=MIDDLE  ALT=\"%283x%2B17%29%2F%28x%5E2%2B10x%2B21%29=%28-4%29%2F%28x%5E2%2B10x%2B21%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since the denominators are equal on both sides, the numerators must be equal as well for the statement to be true, therefore:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B17=-4 ALIGN=MIDDLE  ALT=\"3x%2B17=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x=-21 ALIGN=MIDDLE  ALT=\"3x=-21\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-21%2F3=-7 ALIGN=MIDDLE  ALT=\"x=-21%2F3=-7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "But that causes a problem because -7 is not in the domain of either the y1 or y3 functions.  x=-7 leads to a zero denominator in each case.  Therefore, there are no values of x that satisfy the given conditions.  Presuming my assumptions about the construct of the original problem were correct, that is. </SPAN>\n" );
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