document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=196760>Question 196760</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Simplify each rational expression. State any restrictions on the variable.<BR>\n" );
document.write( "1. 3x^2-12/x^2-x-6<BR>\n" );
document.write( "I got 3(x-2)/(x-3) x cannot be equal to 3 and -2.<BR>\n" );
document.write( "I'm not sure if my restrictions are correct. Could someone please check them?\r<BR>\n" );
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document.write( "Simplify each sum or difference.<BR>\n" );
document.write( "4(x+3)/(x-1)(x+2) + (x-2)(x+3)/(x-1)<BR>\n" );
document.write( "I got 4(x+3)+(x-2)(x+3)/(x-1) which is equivalent to 4(x+3)+x^2+x-6/(x-1)<BR>\n" );
document.write( "I'm not sure if I did this correctly...<BR>\n" );
document.write( "Could someone check?\r<BR>\n" );
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document.write( "Thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #147471 by </B><A HREF=/tutors/aboutme.mpl?userid=RAY100><B>RAY100(1637)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=RAY100><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=147471\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1st  problem<BR>\n" );
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document.write( "Exactly  correct  ,  congrats<BR>\n" );
document.write( "now  @x=-2,  we  have  a  \"hole\" due  to  cancelling (x+2)<BR>\n" );
document.write( "and  at  x=3,  we  have  an  asymptote ,,,,due  to  (x-3)  in  denominator<BR>\n" );
document.write( "zero  at  x=2,  due  to  (x-2)  in num<BR>\n" );
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document.write( "2 nd  problem<BR>\n" );
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document.write( "4 (x+3) / { (x-1) (x+2) }  +  { (x+3) (x-2) } / (x-1)<BR>\n" );
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document.write( "Use  LCD  of  (x-1) (x+2)<BR>\n" );
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document.write( "[  4 (x+3) + { (x+3)(x-2)(x+2) } ] / [ (x-1) (x+2) ]<BR>\n" );
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document.write( "[ (x+3) { 4 + (x-2)(x+2) } ] / (x-1)(x+2)<BR>\n" );
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document.write( "[ (x+3) { 4 + x^2 -4} ] / (x-1)(x+2)<BR>\n" );
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document.write( "{ (x+3) x^2  }/ (x-1)(x+2)<BR>\n" );
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document.write( "(x^3 +3x^2 ) / (x-1)(x+2)<BR>\n" );
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document.write( "Asymptotes  at  x=1,  x=-2,,,,,,due  to  (x-1)(x+2)  in  den<BR>\n" );
document.write( "zero's  at  x=0,,x=-3,,  due  to  factors  in  num<BR>\n" );
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