document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=203380>Question 203380</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do I solve for \"x\" \r<BR>\n" );
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document.write( "(2x)/(x+4)-1/(x-3)=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #153455 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=153455\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%29%2F%28x%2B4%29+-+1%2F%28x-3%29=0 ALIGN=MIDDLE  ALT=\"%282x%29%2F%28x%2B4%29+-+1%2F%28x-3%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The best way to start is to eliminate the fractions. You can eliminate the fractions by multiplying both sides of the equation by the Lowest Common Denominator (LCD) of all the fractions (including, if any fractions on both sides).<BR>\n" );
document.write( "The LCD of the fractions in this equation is: (x+4)(x-3). Multiplying both side by the LCD:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B4%29%28x-3%29%28%282x%29%2F%28x%2B4%29+-+1%2F%28x-3%29%29+=+%28x%2B4%29%28x-3%29%280%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "On the left side we need to use the Distributive Property:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B4%29%28x-3%29%28%282x%29%2F%28x%2B4%29%29+-+%28x%2B4%29%28x-3%29%281%2F%28x-3%29%29+=+%28x%2B4%29%28x-3%29%280%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Simplify<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%28x%2B4%29%28x-3%29%28%282x%29%2F%28cross%28x%2B4%29%29%29+-+%28x%2B4%29cross%28x-3%29%281%2Fcross%28x-3%29%29+=+0 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%282x%29+-+%28x%2B4%29%281%29+=+0 ALIGN=MIDDLE  ALT=\"%28x-3%29%282x%29+-+%28x%2B4%29%281%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2+-+6x+-+%28x%2B4%29+=+0 ALIGN=MIDDLE  ALT=\"2x%5E2+-+6x+-+%28x%2B4%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2+-6x+-+x+-+4+=+0 ALIGN=MIDDLE  ALT=\"2x%5E2+-6x+-+x+-+4+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2+-7x+-4+=+0 ALIGN=MIDDLE  ALT=\"2x%5E2+-7x+-4+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is a quadratic equation. We can solve it by factoring or the Quadratic Formula (or by completing the square). This factors so:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x+%2B+1%29%28x+-+4%29+=+0 ALIGN=MIDDLE  ALT=\"%282x+%2B+1%29%28x+-+4%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "In order for this product to be zero, one of the factors must be zero (Zero Product Property):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+%2B+1+=+0 ALIGN=MIDDLE  ALT=\"2x+%2B+1+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+-+4+=+0 ALIGN=MIDDLE  ALT=\"x+-+4+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Solving each:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-1%2F2 ALIGN=MIDDLE  ALT=\"x+=+-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+4 ALIGN=MIDDLE  ALT=\"x+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So there are two solutions to: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%29%2F%28x%2B4%29+-+1%2F%28x-3%29=0 ALIGN=MIDDLE  ALT=\"%282x%29%2F%28x%2B4%29+-+1%2F%28x-3%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );