document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=189079>Question 189079</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this equation:\r<BR>\n" );
document.write( "\n" );
document.write( "Directions: tell whether the statement is always true, sometimes true, or never true. Explain your reasoning.\r<BR>\n" );
document.write( "\n" );
document.write( "Problem:<BR>\n" );
document.write( "The LCD of two rational expressions is the product of the denominators.\r<BR>\n" );
document.write( "\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 #141827 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=141827\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's look at some examples:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Ex 1: LCD of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fx ALIGN=MIDDLE  ALT=\"1%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%282x%29 ALIGN=MIDDLE  ALT=\"1%2F%282x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x ALIGN=MIDDLE  ALT=\"2x\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Also, the product of the denominators is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2A%282x%29=2x%5E2 ALIGN=MIDDLE  ALT=\"x%2A%282x%29=2x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So in this case, statement is NOT true. So it CANNOT be always true (all it takes is one counter example). So the statement is either sometimes true or never true.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Ex 2: LCD of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2F%283z%29 ALIGN=MIDDLE  ALT=\"y%2F%283z%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2%2F%287w%29 ALIGN=MIDDLE  ALT=\"r%5E2%2F%287w%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=21wz ALIGN=MIDDLE  ALT=\"21wz\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283z%29%287w%29=21wz ALIGN=MIDDLE  ALT=\"%283z%29%287w%29=21wz\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the LCD, this shows us that in this case, the statement is true. So this means that we've eliminated the \"never true\" possibility (as at least one case is true)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So the statement\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "\"The LCD of two rational expressions is the product of the denominators. \"\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "is sometimes true.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Note: the statement is only true if the GCF (or GCD) of the denominators is equal to 1, but we don't have to worry about that technicality.  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );