document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=178970>Question 178970</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find all real solutions of the equation. <BR>\n" );
document.write( " x divided by 2x+6 minus x-9 divided x+5 = 1<BR>\n" );
document.write( "x = ____ (smaller value) <BR>\n" );
document.write( "x = ____(larger value)<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 #133927 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=133927\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large {\frac {x}{2x + 6}}-{\frac {x - 9}{x + 5}} = 1\">\r<BR>\n" );
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document.write( "First find the Lowest Common Denominator.  Since the two denominators have no factors in common, the LCD is simply the product of the two denominators.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac {x (x + 5)} {(2x + 6)(x + 5)} - \frac {(2x + 6)(x - 9)}{(2x + 6)(x + 5)} = \frac {(2x + 6)(x + 5)}{(2x + 6)(x + 5)}\">\r<BR>\n" );
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document.write( "We can simplify this horror by realizing that since the denominators are now equal, we only have to concern ourselves with the sum of the numerators on the left being equal to the numerator on the right.  This is because:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac {a}{d} + \frac {b}{d} = \frac {c}{d} \text{ }\Leftrightarrow \text {} \math a + b = c\">\r<BR>\n" );
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document.write( "So, we can write:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (x (x + 5)) - \[(2x + 6)(x - 9)\] = (2x + 6)(x + 5)\">\r<BR>\n" );
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document.write( "Apply the distributive property and FOIL twice:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x^2 + 5x - (2x^2 - 12x - 54) = 2x^2 + 16x + 30\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x^2 + 5x - 2x^2 + 12x + 54 = 2x^2 + 16x + 30\">\r<BR>\n" );
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document.write( "Collect like terms and put the equation in standard form for a quadratic:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 3x^2 - x - 24 = 0\">\r<BR>\n" );
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document.write( "This actually factors:  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (3x + 8)(x - 3) = 0\">\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x = 3\"> or <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x = -\frac {8}{3}\"><BR>\n" );
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