document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=131900>Question 131900</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I was doing fine on my homework in till I came to a couple of questions that I could not figure out, if you could help me I would really appreciate it. <BR>\n" );
document.write( "Here is the problem 2x+6/x^2-9    +    1/x+3<BR>\n" );
document.write( "I think that if I could find the LCD for the denominators then I could figure out the rest of the problem. I do know that the answers has to be one of these...<BR>\n" );
document.write( "A) 3/x-3<BR>\n" );
document.write( "B) 3(x+1)/(x+3)(x-3)<BR>\n" );
document.write( "C) 3(x+1)/x(x-3)<BR>\n" );
document.write( "D) 2/x-3  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #96418 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=96418\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given to simplify:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%2B6%29%2F%28x%5E2+-+9%29+%2B+1%2F%28x%2B3%29 ALIGN=MIDDLE  ALT=\"%282x%2B6%29%2F%28x%5E2+-+9%29+%2B+1%2F%28x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "The factor form you are looking for is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+-+b%5E2+=+%28a-b%29%2A%28a%2Bb%29 ALIGN=MIDDLE  ALT=\"a%5E2+-+b%5E2+=+%28a-b%29%2A%28a%2Bb%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "The way to look at this is if you have the difference between two perfect squares, it factors into<BR>\n" );
document.write( "the product of the sum and the difference of the two square roots.  Notice that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a <BR>\n" );
document.write( "perfect square and so is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9 ALIGN=MIDDLE  ALT=\"9\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+9 ALIGN=MIDDLE  ALT=\"x%5E2+-+9\"   DISABLED_style= \"max-width:90%; height:auto;\" > factors into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%2A%28x%2B3%29 ALIGN=MIDDLE  ALT=\"%28x-3%29%2A%28x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This makes the <BR>\n" );
document.write( "problem become:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%2B6%29%2F%28%28x-3%29%2A%28x%2B3%29%29+%2B+1%2F%28x%2B3%29 ALIGN=MIDDLE  ALT=\"%282x%2B6%29%2F%28%28x-3%29%2A%28x%2B3%29%29+%2B+1%2F%28x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "You can now put the second fraction over a common denominator of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%2A%28x%2B3%29 ALIGN=MIDDLE  ALT=\"%28x-3%29%2A%28x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > by <BR>\n" );
document.write( "multiplying the second fraction by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%2F%28x-3%29 ALIGN=MIDDLE  ALT=\"%28x-3%29%2F%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to make the problem:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%2B6%29%2F%28%28x-3%29%2A%28x%2B3%29%29+%2B+%281%2F%28x%2B3%29%29%2A%28%28x-3%29%2F%28x-3%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "and this makes the problem become:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%2B6%29%2F%28%28x-3%29%2A%28x%2B3%29%29+%2B+%28x-3%29%2F%28%28x-3%29%2A%28x%2B3%29%29 ALIGN=MIDDLE  ALT=\"%282x%2B6%29%2F%28%28x-3%29%2A%28x%2B3%29%29+%2B+%28x-3%29%2F%28%28x-3%29%2A%28x%2B3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Since the two fractions now have a common denominator, you can combine their two numerators over<BR>\n" );
document.write( "the common denominator and you have:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x+%2B+6+%2B+x+-+3%29%2F%28%28x-3%29%2A%28x%2B3%29%29 ALIGN=MIDDLE  ALT=\"%282x+%2B+6+%2B+x+-+3%29%2F%28%28x-3%29%2A%28x%2B3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "In the numerator combine the 2x and + x to get 3x and also combine the +6 and -3 to get +3.<BR>\n" );
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document.write( "This makes the fraction become:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x+%2B+3%29%2F%28%28x+-3%29%2A%28x%2B3%29%29 ALIGN=MIDDLE  ALT=\"%283x+%2B+3%29%2F%28%28x+-3%29%2A%28x%2B3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Notice that the numerator can be factored by taking out a 3 to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%28x%2B1%29%29%2F%28%28x+-3%29%2A%28x%2B3%29%29 ALIGN=MIDDLE  ALT=\"%283%28x%2B1%29%29%2F%28%28x+-3%29%2A%28x%2B3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "This looks like answer B on your answer list.<BR>\n" );
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document.write( "Hope this helps you to understand the problem and how to work it.<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );