document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1108819>Question 1108819</A>: <I><SPAN STYLE=\"word-break: break-all;\"> denominator of a fraction is 2 more than the numerator if the sum of fraction and its denominator is 28/5 find the fraction </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #723818 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=723818\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x equal the numerator.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "then x + 2 equal the denominator.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your equation becomes (x/(x+2) + (x+2) = 28/5.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "multiply both sides of this equation by (x+2) and you get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x + (x+2)^2 = 28/5 * (x+2).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "multiply both sides of this equation by 5 to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "5 * (x + (x+2)^2) = 28 * (x+2)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since (x+2)^2  x^2 + 4x + 4, this equation can be simplified to:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "5 * (x + x^2 + 4x + 4) = 28 * (x + 2)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "combine like terms to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "5 * (x^2 + 5x + 4) = 28 * (x + 2)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since 28 * (x + 2) is equal to 28 * x + 56, this equation becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "5 * (x^2 + 5x + 4) = 28 * x + 56\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since 5 * (x^2 + 5x + 4) = 5 * x^2 + 25 * x + 20, this equation becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "5 * x^2 + 25 * x + 20 = 28 * x + 56\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "subtract 28 * x and subtract 56 from both sides of this equation to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "5 * x^2 - 3 * x - 36 = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "factor this quadratic equation to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x = 3 or x = -2.4\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "replace x with 3 and then replace x with -2.4 to see which of these, if not both, are solutions to this problem.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "when x = 3, the original equation of (x/(x+2)) + (x+2) = 28/5 becomes (3/5) + 5 = 5.6 which is equal to 28/5.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you can use your calculator to confirm that 28/5 = 5.6.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "when x = -2.4, the original equation (x/(x+2)) + (x+2) = 28/5 becomes (-2.4/-.4) -2.4 + 2 which is equal to 5.6.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "looks like both values of x satisfy the original equation, so the solution is that x can be 3 or x = -2.4.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you can also check by graphing the equations of:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "y = (x/(x+2)) + (x+2) and y = 28/5, and then looking for the intersection of those 2 equations.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the intersections confirm the algebra.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the graph looks like this:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src= \"http://theo.x10hosting.com/2018/020702.jpg\" alt=\"$$$\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );