document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=35754>Question 35754</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (x+4)/10=6/(x-3) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #21871 by </B><A HREF=/tutors/aboutme.mpl?userid=kev82><B>kev82(151)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=kev82><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=21871\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi,\r<BR>\n" );
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document.write( "We want to find x. At the moment x is in the numerator of one fraction, and the denominator of another. There are a few ways to solve this, but the simplest is to get rid of fractions all together, by multiplying the whole equation by <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?10(x-3)\">. This gives us\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?(x-3)(x+4)=60\">\r<BR>\n" );
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document.write( "Think about what we've just done if <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?x=3\">, Does it matter?\r<BR>\n" );
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document.write( "We're now left with this equation, which is your bog standard quadratic. This one can be factorised quite easily. (I miss the days when every quadratic I had to solve was factorisable!)\r<BR>\n" );
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document.write( "Multiplying out and tidying up gives\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?x^2+x-72=0\">\r<BR>\n" );
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document.write( "Now, there isn't any coeficient in front of the x, and the constant term is negative, so we're looking at something like:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?(x+?_1)(x-?_2)=0\">\r<BR>\n" );
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document.write( "Where the question marks multiply to 72, and have a difference of 1. 8, and 9 look like good candidates. So that gives\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?(x+9)(x-8)=0\">\r<BR>\n" );
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document.write( "So from this we can read off that either <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?x=-9\"> or <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?x=8\">\r<BR>\n" );
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document.write( "Pluging both of these into the original equation shows they both work, so there's your answers.\r<BR>\n" );
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document.write( "Hope that helps,<BR>\n" );
document.write( "Kev </SPAN>\n" );
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