document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=271386>Question 271386</A>: <I><SPAN STYLE=\"word-break: break-all;\"> simplify:<BR>\n" );
document.write( "4n/ n squared - 4  minus 2/n + 2  minus 2/n + 2\r<BR>\n" );
document.write( "\n" );
document.write( "a. 2/n - 2<BR>\n" );
document.write( "b. 4n - 2/n squared - n - 6<BR>\n" );
document.write( "c. 2/n + 2<BR>\n" );
document.write( "d. 1/n - 1<BR>\n" );
document.write( "Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #199192 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=199192\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284n%29%2F%28n%5E2-+4%29+-+2%2F%28n+%2B+2%29+-+2%2F%28n+%2B+2%29 ALIGN=MIDDLE  ALT=\"%284n%29%2F%28n%5E2-+4%29+-+2%2F%28n+%2B+2%29+-+2%2F%28n+%2B+2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since subtractions can a source of errors for many people, I am going to start by changing the subtractions into additions:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284n%29%2F%28n%5E2-+4%29+%2B+%28-2%29%2F%28n+%2B+2%29+%2B+%28-2%29%2F%28n+%2B+2%29 ALIGN=MIDDLE  ALT=\"%284n%29%2F%28n%5E2-+4%29+%2B+%28-2%29%2F%28n+%2B+2%29+%2B+%28-2%29%2F%28n+%2B+2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and the last two terms have the same denominator so I will go ahead and add them:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284n%29%2F%28n%5E2-+4%29+%2B+%28-4%29%2F%28n+%2B+2%29 ALIGN=MIDDLE  ALT=\"%284n%29%2F%28n%5E2-+4%29+%2B+%28-4%29%2F%28n+%2B+2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "To add the remaining fractions we need to get a common denominator first. And to find the Lowest Common Denominator (LCD) we need to factor each denominator:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284n%29%2F%28%28n%2B2%29%28n+-+2%29%29+%2B+%28-4%29%2F%28n+%2B+2%29 ALIGN=MIDDLE  ALT=\"%284n%29%2F%28%28n%2B2%29%28n+-+2%29%29+%2B+%28-4%29%2F%28n+%2B+2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "From this we can see that<ul><li>the LCD is (n+2)(n-2)</li><li>the first fraction already has the LCD as the denominator</li><li>the part of the LCD missing in the second denominator is n-2</li></ul><BR>\n" );
document.write( "So we will multiply the numerator and denominator of the second fraction by n-2:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284n%29%2F%28%28n%2B2%29%28n+-+2%29%29+%2B+%28%28-4%29%2F%28n+%2B+2%29%29%28%28n-2%29%2F%28n-2%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which simplifies to:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284n%29%2F%28%28n%2B2%29%28n+-+2%29%29+%2B+%28-4n+%2B+8%29%2F%28n+%2B+2%29%28n-2%29%29 ALIGN=MIDDLE  ALT=\"%284n%29%2F%28%28n%2B2%29%28n+-+2%29%29+%2B+%28-4n+%2B+8%29%2F%28n+%2B+2%29%28n-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we can add the fractions. (Leave the denominators factored for now.):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2F%28%28n%2B2%29%28n+-+2%29%29 ALIGN=MIDDLE  ALT=\"8%2F%28%28n%2B2%29%28n+-+2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which does not match any of the provided answers. I don't see any errors so I must assume that there is something wrong in the problem you posted. I'm going to guess that the denominator of one of the last two fractions should be n-2 and not n+2. So I am going to solve the problem again with a n-2 denominator. (It doesn't matter which fraction because they are both the same.) I am not going to provide commentary this time. The logic is the same as above except, since the last two fractions no longer have the same denominator to start with, I will not be adding the last two fractions so early.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284n%29%2F%28n%5E2-+4%29+-+2%2F%28n+%2B+2%29+-+2%2F%28n+-+2%29 ALIGN=MIDDLE  ALT=\"%284n%29%2F%28n%5E2-+4%29+-+2%2F%28n+%2B+2%29+-+2%2F%28n+-+2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284n%29%2F%28n%5E2-+4%29+%2B+%28-2%29%2F%28n+%2B+2%29+%2B+%28-2%29%2F%28n+-+2%29 ALIGN=MIDDLE  ALT=\"%284n%29%2F%28n%5E2-+4%29+%2B+%28-2%29%2F%28n+%2B+2%29+%2B+%28-2%29%2F%28n+-+2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284n%29%2F%28%28n%2B2%29%28n-2%29%29+%2B+%28-2%29%2F%28n+%2B+2%29+%2B+%28-2%29%2F%28n+-+2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284n%29%2F%28%28n%2B2%29%28n-2%29%29+%2B+%28%28-2%29%2F%28n+%2B+2%29%29%28%28n-2%29%2F%28n-2%29%29+%2B+%28%28-2%29%2F%28n+-+2%29%29%28%28n%2B2%29%2F%28n%2B2%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284n%29%2F%28%28n%2B2%29%28n-2%29%29+%2B+%28-2n%2B4%29%2F%28%28n+%2B+2%29%28n-2%29%29+%2B+%28-2n-4%29%2F%28%28n%2B2%29%28n-2%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%2F%28%28n%2B2%29%28n-2%29%29 ALIGN=MIDDLE  ALT=\"0%2F%28%28n%2B2%29%28n-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which doesn't match any of the provided answers either. I still see no errors in my work so I have to assume that either the provided answers are in correct or both the original equation and the one I guessed at are also wrong. But perhaps you have seen enough here to figure out the actual problem. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );