document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=166719>Question 166719</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how do you simplify this rational expression?\r<BR>\n" );
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document.write( "(2/k-3)+ (4/k+3)=\r<BR>\n" );
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document.write( "i was out sick for 3 days and i dont know how to do this. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #122867 by </B><A HREF=/tutors/aboutme.mpl?userid=MRperkins><B>MRperkins(300)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MRperkins><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/cgi-bin/show-face.mpl?user=MRperkins><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=122867\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here is a quick lesson for you.  First, think about fractions you can check for accuracy.  Let's look at adding 2/3 and 3/4. <BR>\n" );
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document.write( "We know that we can not add these two numbers as they are because they do not have the same denominator (the bottom number).  <BR>\n" );
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document.write( "So, we need to find a way to get the denominators to be the same.  This is done by finding something called the least common multiple or LCM.  <BR>\n" );
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document.write( "The LCM will always contain the denominator of each term.<BR>\n" );
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document.write( "The LCM of 2/3 and 3/4 is 12 so you multiply 2/3 by 4/4 and you get 8/12.<BR>\n" );
document.write( "multiply 3/4 by 3/3 and you get 9/12.  Now you can add 8/12 and 9/12 together to get 17/12.<BR>\n" );
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document.write( "For your problem: the LCM is (k-3)*(k+3)<BR>\n" );
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document.write( "Whenever both fractions have the LCM as the denominator then you will be able to add them together.<BR>\n" );
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document.write( "In order to make the first term have (k-3)(k+3) you need to multiply the top and bottom (numerator and denominator) by (k+3).  This is equivalent to multiplying the term by 1 because anything divided by itself is 1.<BR>\n" );
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document.write( "So you have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%28k%2B3%29%29%2F%28%28k-3%29%28k%2B3%29%29 ALIGN=MIDDLE  ALT=\"%282%28k%2B3%29%29%2F%28%28k-3%29%28k%2B3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You need to do the same thing with the second fraction<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%28k-3%29%29%2F%28%28k%2B3%29%28k-3%29%29 ALIGN=MIDDLE  ALT=\"%284%28k-3%29%29%2F%28%28k%2B3%29%28k-3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "now you can add the two fractions together<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%28k%2B3%29%29%2F%28%28k-3%29%28k%2B3%29%29%2B%284%28k-3%29%29%2F%28%28k%2B3%29%28k-3%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "notice on the sample problem that when adding 8 twelths and 9 twelths you get 17 twelths.  The denominator stays the same when adding.<BR>\n" );
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document.write( "So:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%28k%2B3%29%29%2F%28%28k-3%29%28k%2B3%29%29%2B%284%28k-3%29%29%2F%28%28k%2B3%29%28k-3%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > can be written by adding the numerators over the same denominator like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%282%28k%2B3%29%29%2B%284%28k-3%29%29%29%2F%28%28k-3%29%28k%2B3%29%29 ALIGN=MIDDLE  ALT=\"%28%282%28k%2B3%29%29%2B%284%28k-3%29%29%29%2F%28%28k-3%29%28k%2B3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "remember (P)lease Excuse My Dear Aunt Sally for your order of operations<BR>\n" );
document.write( "Parenthesis/Exponents<BR>\n" );
document.write( "Multiply/Divide<BR>\n" );
document.write( "Add/Subtract<BR>\n" );
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document.write( "You are probably good once you get to this point so I will just show the final steps.<BR>\n" );
document.write( "Distribute the 2 and the 4<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282k%2B6%2B4k-12%29%2F%28%28k-3%29%28k%2B3%29%29 ALIGN=MIDDLE  ALT=\"%282k%2B6%2B4k-12%29%2F%28%28k-3%29%28k%2B3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "combine like terms<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286k-6%29%2F%28%28k-3%29%28k%2B3%29%29 ALIGN=MIDDLE  ALT=\"%286k-6%29%2F%28%28k-3%29%28k%2B3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "factor out a 6<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286%28k-1%29%29%2F%28%28k-3%29%28k%2B3%29%29 ALIGN=MIDDLE  ALT=\"%286%28k-1%29%29%2F%28%28k-3%29%28k%2B3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "If you have any questions, email me at justin.sheppard.tech@hotmail.com </SPAN>\n" );
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