document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=232481>Question 232481</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve for the variable, first stating any restrictions. if there are no restrictions, state that<BR>\n" );
document.write( "7/x+4 + 2/x-3 = 7x-21/x^2+x-12 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #171791 by </B><A HREF=/tutors/aboutme.mpl?userid=eggsarecool><B>eggsarecool(46)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=eggsarecool><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=171791\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I am assuming this is the original problem, it wasn't completely clear.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2F%28x%2B4%29+%2B+2%2F%28x-3%29+=+%287x-21%29%2F%28x%5E2%2Bx-12%29 ALIGN=MIDDLE  ALT=\"7%2F%28x%2B4%29+%2B+2%2F%28x-3%29+=+%287x-21%29%2F%28x%5E2%2Bx-12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > the next step is to rewrite the right hand side.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2F%28x%2B4%29+%2B+2%2F%28x-3%29+=+%287x-21%29%2F%28x%2B4%29%28x-3%29 ALIGN=MIDDLE  ALT=\"7%2F%28x%2B4%29+%2B+2%2F%28x-3%29+=+%287x-21%29%2F%28x%2B4%29%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now we state the restrictions, these happen when you divide by 0. So x cannot equal to 3 or -4\r<BR>\n" );
document.write( "\n" );
document.write( "Your next step is to create a common denominator on the left side.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%28x-3%29%2F%28x%2B4%29%28x-3%29%2B2%28x%2B4%29%2F%28x%2B4%29%28x-3%29=%287x-21%29%2F%28x%2B4%29%28x-3%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we will only pay attention to the numerators since the denominators match.<BR>\n" );
document.write( "This gives us.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x-21%2B2x%2B8=7x-21 ALIGN=MIDDLE  ALT=\"7x-21%2B2x%2B8=7x-21\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now combine like terms.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9x-13=7x-21 ALIGN=MIDDLE  ALT=\"9x-13=7x-21\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "subtract 9x from both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-13=-21 ALIGN=MIDDLE  ALT=\"2x-13=-21\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "add 13 to both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x=-8 ALIGN=MIDDLE  ALT=\"2x=-8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Divide both sides by 2.<BR>\n" );
document.write( "<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( "This gives you the solution <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;\" > but since this is among the values that are not allowed your equation has no solution. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );