document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=88743>Question 88743</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me to simplify each complex fraction and reduce each answer to lowest terms:\r<BR>\n" );
document.write( "\n" );
document.write( "42)     1/3+1/y  over  y/3-3/y\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "and \r<BR>\n" );
document.write( "\n" );
document.write( "50)     ab+b^2/4ab^5  over  a+b/6a^2b^4\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Thank you very much! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #64501 by </B><A HREF=/tutors/aboutme.mpl?userid=chitra><B>chitra(359)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=chitra><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=64501\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 42)  The given expression is:  \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F3%29+%2B+%281%2Fy%29 ALIGN=MIDDLE  ALT=\"%281%2F3%29+%2B+%281%2Fy%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > over <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%2F3%29+-+%283%2Fy%29 ALIGN=MIDDLE  ALT=\"%28y%2F3%29+-+%283%2Fy%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%281%2F3%29+%2B+%281%2Fy%29%29%2F%28%28y%2F3%29+-+%283%2Fy%29%29 ALIGN=MIDDLE  ALT=\"%28%281%2F3%29+%2B+%281%2Fy%29%29%2F%28%28y%2F3%29+-+%283%2Fy%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Taking LCM on both the numerator and the denominator, we get: \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28y+%2B+3%29%2F3y%29%2F%28%28y%5E2+-+9%29%2F3y%29 ALIGN=MIDDLE  ALT=\"%28%28y+%2B+3%29%2F3y%29%2F%28%28y%5E2+-+9%29%2F3y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Simplifying the term in the denominator, we get: \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28y+%2B+3%29%2F3y%29%2F%28%28y+-+3%29%28y+%2B+3%29%2F3y%29 ALIGN=MIDDLE  ALT=\"%28%28y+%2B+3%29%2F3y%29%2F%28%28y+-+3%29%28y+%2B+3%29%2F3y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This can be written as:  \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28%28y+%2B+3%29%2F3y%29+%2A+%28%283y%29%2F%28y+%2B+3%29%28y+-+3%29%29+ ALIGN=MIDDLE  ALT=\"+%28%28y+%2B+3%29%2F3y%29+%2A+%28%283y%29%2F%28y+%2B+3%29%28y+-+3%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Cancelling out terms, we get: \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28y+-+3%29 ALIGN=MIDDLE  ALT=\"1%2F%28y+-+3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Hence, the solution. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "================================================================================\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "50) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28ab+%2B+b%5E2%29%2F4ab%5E5 ALIGN=MIDDLE  ALT=\"%28ab+%2B+b%5E2%29%2F4ab%5E5\"   DISABLED_style= \"max-width:90%; height:auto;\" >  over  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a+%2B+b%29%2F%286a%5E2b%5E4%29 ALIGN=MIDDLE  ALT=\"%28a+%2B+b%29%2F%286a%5E2b%5E4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This can be written as: \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28ab+%2B+b%5E2%29%2F%284ab%5E5%29%29+%2F%28%28a+%2B+b%29%2F%286a%5E2b%5E4%29%29 ALIGN=MIDDLE  ALT=\"%28%28ab+%2B+b%5E2%29%2F%284ab%5E5%29%29+%2F%28%28a+%2B+b%29%2F%286a%5E2b%5E4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Taking \"b\" as the common factor, we get: \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28b%28a+%2B+b%29%2F%284ab%5E5%29%29+%2F%28%28a+%2B+b%29%2F%286a%5E2b%5E4%29%29 ALIGN=MIDDLE  ALT=\"%28b%28a+%2B+b%29%2F%284ab%5E5%29%29+%2F%28%28a+%2B+b%29%2F%286a%5E2b%5E4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This can be written as:  \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28b%28a+%2B+b%29%2F%284ab%5E5%29%29+%2A+%28%286a%5E2b%5E4%29%2F%28a+%2B+b%29%29 ALIGN=MIDDLE  ALT=\"%28b%28a+%2B+b%29%2F%284ab%5E5%29%29+%2A+%28%286a%5E2b%5E4%29%2F%28a+%2B+b%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Cancelling out common terms, we get: \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2F2%29a ALIGN=MIDDLE  ALT=\"%283%2F2%29a\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Hence, the solution. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Regards\r<BR>\n" );
document.write( "\n" );
document.write( "Chitra<BR>\n" );
document.write( "Online Math Tutor<BR>\n" );
document.write( "chitra@knowledgeonlineservices.com\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );