document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=388168>Question 388168</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the denominator of the fraction is 2 more than the numerator. if 1 is subtracted from both numerator and denominator, the resulting fraction has a value of 1/2. find the original fraction </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #274466 by </B><A HREF=/tutors/aboutme.mpl?userid=aggie_tutor><B>aggie_tutor(13)</B></A><img src=\"/images/stars/stars-06.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=aggie_tutor><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/cgi-bin/show-face.mpl?user=aggie_tutor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=274466\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let numerator = x<BR>\n" );
document.write( "Problem statment: demoninator = (x+2)<BR>\n" );
document.write( "So the fraction looks like:<BR>\n" );
document.write( "x/(x+2)\r<BR>\n" );
document.write( "\n" );
document.write( "Second part of problem statement: <BR>\n" );
document.write( "Numerator (x-1)<BR>\n" );
document.write( "Denominator (x+2)-1\r<BR>\n" );
document.write( "\n" );
document.write( "So the new fraction (forget about the old one!) looks like:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29%2F%28x%2B2-1%29 ALIGN=MIDDLE  ALT=\"%28x-1%29%2F%28x%2B2-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "For subtraction simplifies to:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29%2F%28x%2B1%29 ALIGN=MIDDLE  ALT=\"%28x-1%29%2F%28x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Set the equation. Problem statement says this fraction thing is equal to 1/2.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29%2F%28x%2B1%29+=+1%2F2 ALIGN=MIDDLE  ALT=\"%28x-1%29%2F%28x%2B1%29+=+1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "The 1/2 fraction doesn't look too nice so let's just make it 1. We can do that by multiplying both sides of the equation by 2, i.e. 2/1.\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2F1%29%28%28x-1%29%2F%28x%2B1%29%29+=+%282%2F1%29%281%2F2%29 ALIGN=MIDDLE  ALT=\"%282%2F1%29%28%28x-1%29%2F%28x%2B1%29%29+=+%282%2F1%29%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "The right side just becomes 1 (the 2s cancel out.)<BR>\n" );
document.write( "The left side is tricky. You must multiply the numerator by 2 only.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%29%2A%28x-1%29 ALIGN=MIDDLE  ALT=\"%282%29%2A%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-2 ALIGN=MIDDLE  ALT=\"2x-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "The denominator is multiplied by 1, so it does not change at all. <BR>\n" );
document.write( "The new left side and right side of the equation is now:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x-2%29%2F%28x%2B1%29+=+1 ALIGN=MIDDLE  ALT=\"%282x-2%29%2F%28x%2B1%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Much nicer to look at. And when we have a fraction = 1, we can always multiply both sides by the denominator (x+1). This cancels the denominator on the left, and moves the (x+1) to the right side. This gets rid of the fraction, which is what we wanted.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B1%29%28%282x-2%29%2F%28x%2B1%29%29+=+%28x%2B1%29%281%29 ALIGN=MIDDLE  ALT=\"%28x%2B1%29%28%282x-2%29%2F%28x%2B1%29%29+=+%28x%2B1%29%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x-2%29+=+%28x%2B1%29 ALIGN=MIDDLE  ALT=\"%282x-2%29+=+%28x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-2+=+x%2B1 ALIGN=MIDDLE  ALT=\"2x-2+=+x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Combine like terms. We can put x terms on the left, and the constant (non-x) terms on the right. First subtract x from both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-2-x+=+x-x%2B1 ALIGN=MIDDLE  ALT=\"2x-2-x+=+x-x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-2+=+1 ALIGN=MIDDLE  ALT=\"x-2+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now add 2 to both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-2%2B2+=+1%2B2 ALIGN=MIDDLE  ALT=\"x-2%2B2+=+1%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+3 ALIGN=MIDDLE  ALT=\"x+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Check your answer by putting x into the original equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29%2F%28x%2B1%29+=+1%2F2 ALIGN=MIDDLE  ALT=\"%28x-1%29%2F%28x%2B1%29+=+1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283-1%29%2F%283%2B1%29+=+1%2F2 ALIGN=MIDDLE  ALT=\"%283-1%29%2F%283%2B1%29+=+1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%29%2F%284%29+=+1%2F2 ALIGN=MIDDLE  ALT=\"%282%29%2F%284%29+=+1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );