document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=240581>Question 240581</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The problem is: (x+5)/3 + 4/x = 5/6  My instructions are to use the quadratic formula to solve. I think I am supposed to multiply by the common denominator, but I am not sure.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #176319 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=176319\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You are correct. Probably the easiest way to proceed is to multiply both sides of the equation by the Lowest Common Denominator (LCD) of all the denominators. The LCD of 3, x and 6 is 6x so we'll multiply both sides by 6x:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%28%28x%2B5%29%2F3+%2B+4%2Fx%29+=+6x%285%2F6%29 ALIGN=MIDDLE  ALT=\"6x%28%28x%2B5%29%2F3+%2B+4%2Fx%29+=+6x%285%2F6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "On the left side we use the Distributive Property to multiply:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%28%28x%2B5%29%2F3%29+%2B+6x%284%2Fx%29+=+6x%285%2F6%29 ALIGN=MIDDLE  ALT=\"6x%28%28x%2B5%29%2F3%29+%2B+6x%284%2Fx%29+=+6x%285%2F6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The denominator of each fraction cancels with some part of 6x leaving:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%28x%2B5%29+%2B+6%284%29+=+x%285%29 ALIGN=MIDDLE  ALT=\"2x%28x%2B5%29+%2B+6%284%29+=+x%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Simplifying this we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2+%2B+5x+%2B+24+=+5x ALIGN=MIDDLE  ALT=\"2x%5E2+%2B+5x+%2B+24+=+5x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since this is a quadratic equation we will solve it by<BR>\n" );
document.write( "1) Get one side equal to zero<BR>\n" );
document.write( "Subtracting 5x from each side we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2+%2B+24+=+0 ALIGN=MIDDLE  ALT=\"2x%5E2+%2B+24+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2) Either factor or use the quadratic formula. We can factor out a 2:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28x%5E2+%2B+12%29+=+0 ALIGN=MIDDLE  ALT=\"2%28x%5E2+%2B+12%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "As a sum of squares, there is no way to factor the 2nd factor any further. The only solutions to this equation then are the x's that make <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+12 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+12\"   DISABLED_style= \"max-width:90%; height:auto;\" > equal to zero. But if we think about it, we'll realize that there are no (Real) numbers that will make <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+12 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+12\"   DISABLED_style= \"max-width:90%; height:auto;\" > equal to zero. This is so because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > would have to be -12 and there are no Real numbers that you can square and get a negative number like -12.<br><BR>\n" );
document.write( "So your equation has no Real solutions. (If you are supposed to find Complex solutions, just use simplify <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28-12%29 ALIGN=MIDDLE  ALT=\"sqrt%28-12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.)<BR>\n" );
document.write( " </SPAN>\n" );
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