document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=553439>Question 553439</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help solving this equation, we have been working on factoring and I can't seem to find a solution for this equation, please help! Thanks!\r<BR>\n" );
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document.write( "Solve:  6/(y-2)+7/(y-8)=(y-1)/(y-8) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #360835 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=360835\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your original equation is:<BR>\n" );
document.write( "6/(y-2) + 7/(y-8) = (y-1)/(y-8)<BR>\n" );
document.write( "multiply both sides of this equation by (y-2)(y-8) to get:<BR>\n" );
document.write( "6(y-8) + 7(y-2) = (y-1)(y-2)<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "6y - 48 + 7y - 14 = y^2 - 3y + 2<BR>\n" );
document.write( "simplify by combining like terms to get:<BR>\n" );
document.write( "13y - 62 = y^2 - 3y + 2<BR>\n" );
document.write( "subtract 13y and add 62 to both sides of the equation to get:<BR>\n" );
document.write( "0 = y^2 - 16y + 64<BR>\n" );
document.write( "commute to get:<BR>\n" );
document.write( "y^2 - 16y + 64 = 0<BR>\n" );
document.write( "that's your quadratic equation which can now be factored to:<BR>\n" );
document.write( "(y-8)^2 = 0 which becomes:<BR>\n" );
document.write( "(y-8)(y-8) = 0 which yields:<BR>\n" );
document.write( "y = 8<BR>\n" );
document.write( "that's your answer until you plug that answer back into the original equation.<BR>\n" );
document.write( "then you get a nasty surprise because x = 8 is undefined in the original equation because it makes the denominator equal to 0.<BR>\n" );
document.write( "that means that there is no real solution to your original equation.<BR>\n" );
document.write( "x = 8 is a good answer for y^2 - 16y + 64 because it does yield the root at x = 8.<BR>\n" );
document.write( "when you graph the quadratic equation, you get something that looks like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-2%2C12%2C-2%2C12%2Cx%5E2-16x%2B64%2C200%28x-8%29%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-2%2C12%2C-2%2C12%2Cx%5E2-16x%2B64%2C200%28x-8%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "note that i had to replace y with x in order to graph it.<BR>\n" );
document.write( "note that the graph of the equation crosses the x-axis at x = 8.<BR>\n" );
document.write( "that's the root of the quadratic equation.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "when you graph the original equation, you get something very different that looks like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-2%2C20%2C-75%2C75%2C6%2F%28x-2%29%2B7%2F%28x-8%29-%28x-1%29%2F%28x-8%29%2C1000%28x-8%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "note that the graph does cross the x-axis at x = 8.<BR>\n" );
document.write( "the problem is that the value of y is undefined in the original equation when x = 8 resulting in what is called a hole.  <BR>\n" );
document.write( "a hole is a gap in the value of y.<BR>\n" );
document.write( "you have values of y all around that spot, but you do not have a value for y when x = 8.<BR>\n" );
document.write( "note again that your original equation was expressed with the variable of y but that i changed y to x in order to be able to graph it.<BR>\n" );
document.write( "when you graph the equation, x is the independent variable and y is the dependent variable.<BR>\n" );
document.write( "that has something to do with the software only being able to recognize x on the horizontal axis and y on the vertical axis.  <BR>\n" );
document.write( "if you were drawing the draph manually, then you could have assigned horizontal to z and vertical to z or any other letter.<BR>\n" );
document.write( "you do have an answer for your quadratic equation.<BR>\n" );
document.write( "that answer is 8.<BR>\n" );
document.write( "you do not have an answer for the original equation because x = 8 (rather y = 8) is not defined in the original equation.\r<BR>\n" );
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