document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1120354>Question 1120354</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve the equation and show the check of your solutions:<BR>\n" );
document.write( "3x over x-4 minus 6 over x^2-7x+12 equal 2x over x-3\r<BR>\n" );
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document.write( "3x/x-4 - 6/x^2-7x+12 = 2x/x-3 </SPAN>\n" );
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document.write( "3x/x-4 - 6/x^2-7x+12 = 2x/x-3<BR>\n" );
document.write( "note that x^2-7x+12 is also (x-4)(x-3)<BR>\n" );
document.write( "multiply both sides by x^2-7x+12<BR>\n" );
document.write( "this becomes<BR>\n" );
document.write( "3x(x-3)-6=2x(x-4)<BR>\n" );
document.write( "3x^2-9x-6=2x^2-8x<BR>\n" );
document.write( "x^2-x-6=0<BR>\n" );
document.write( "(x-3)(x+2)=0<BR>\n" );
document.write( "x=3 and -2<BR>\n" );
document.write( "x=3 is extraneous, because two terms will have 0 in the denominator.<BR>\n" );
document.write( "x=-2 is the solution\r<BR>\n" );
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document.write( "Check<BR>\n" );
document.write( "-6/-6 minus 6/30=-4/-5<BR>\n" );
document.write( "1-0.2=0.8 checks. </SPAN>\n" );
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