document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=369132>Question 369132</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Simplify\r<BR>\n" );
document.write( "\n" );
document.write( "1/a+b - 1/a-b divided by 1/a-b + 1/a+b </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #263264 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=263264\">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=%281%2F%28a%2Bb%29+-+1%2F%28a-b%29%29%2F%281%2F%28a-b%29+%2B+1%2F%28a%2Bb%29%29 ALIGN=MIDDLE  ALT=\"%281%2F%28a%2Bb%29+-+1%2F%28a-b%29%29%2F%281%2F%28a-b%29+%2B+1%2F%28a%2Bb%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Because subtraction of fractions can cause many errors, I like to change them into additions of the opposite:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F%28a%2Bb%29+%2B+%28-1%29%2F%28a-b%29%29%2F%281%2F%28a-b%29+%2B+1%2F%28a%2Bb%29%29 ALIGN=MIDDLE  ALT=\"%281%2F%28a%2Bb%29+%2B+%28-1%29%2F%28a-b%29%29%2F%281%2F%28a-b%29+%2B+1%2F%28a%2Bb%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "There are several ways to simplify this expression. The way I like to do this is:<ol><li>Find the Lowest Common Denomintor (LCD) of all the \"little\" denominators.</li><li>Multiply the numerator and denominator of the \"big\" fraction by the LCD found in step 1.</li></ol><BR>\n" );
document.write( "Let's see how this works on your problem.<BR>\n" );
document.write( "1) Find the LCD of the \"little\" denominators. The \"little\" denominators are (a+b) and (a-b). The LCD of these two is simply their product: (a+b)(a-b)<BR>\n" );
document.write( "2) Multiply the numerator and denominator of the \"big\" fraction by the LCD:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%281%2F%28a%2Bb%29+%2B+%28-1%29%2F%28a-b%29%29%2F%281%2F%28a-b%29+%2B+1%2F%28a%2Bb%29%29%29%2A%28%28%28a%2Bb%29%28a-b%29%29%2F%28%28a%2Bb%29%28a-b%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "In both the numerator and denominator we will need to use the Distributive Property to multiply:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%281%2F%28a%2Bb%29%29%2A%28a%2Bb%29%28a-b%29+%2B+%28%28-1%29%2F%28a-b%29%29%2A%28a%2Bb%29%28a-b%29%29%2F%28%281%2F%28a-b%29%29%2A%28a%2Bb%29%28a-b%29+%2B+%281%2F%28a%2Bb%29%29%2A%28a%2Bb%29%28a-b%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now <i>all</i> the \"little\" denominators cancel out:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%281%2Fcross%28%28a%2Bb%29%29%29%2Across%28%28a%2Bb%29%29%28a-b%29+%2B+%28%28-1%29%2Fcross%28%28a-b%29%29%29%2A%28a%2Bb%29cross%28%28a-b%29%29%29%2F%28%281%2Fcross%28%28a-b%29%29%29%2A%28a%2Bb%29cross%28%28a-b%29%29+%2B+%281%2Fcross%28%28a%2Bb%29%29%29%2Across%28%28a%2Bb%29%29%28a-b%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "leaving:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2A%28a-b%29+%2B+%28-1%29%2A%28a%2Bb%29%29%2F%281%2A%28a%2Bb%29+%2B+1%2A%28a-b%29%29 ALIGN=MIDDLE  ALT=\"%281%2A%28a-b%29+%2B+%28-1%29%2A%28a%2Bb%29%29%2F%281%2A%28a%2Bb%29+%2B+1%2A%28a-b%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which simplifies as follows:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a+-+b+%2B+%28-a%29+%2B+%28-b%29%29%2F%28a+%2B+b+%2B+a+-+b%29 ALIGN=MIDDLE  ALT=\"%28a+-+b+%2B+%28-a%29+%2B+%28-b%29%29%2F%28a+%2B+b+%2B+a+-+b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-2b%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"%28-2b%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The 2's cancel leaving<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-b%29%2Fa ALIGN=MIDDLE  ALT=\"%28-b%29%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );