document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1048230>Question 1048230</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Consider the following equation:<BR>\n" );
document.write( "[&#946;/( &#946; – 2)] + 2 = (2&#946; – 2)/( &#946; – 2)<BR>\n" );
document.write( "Is &#946; = 2 a root of the original equation? If not, why? Discuss the importance of excluding <BR>\n" );
document.write( "values that make a denominator 0 when solving equations.   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #663834 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=663834\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> [b/( b – 2)] + 2 = (2b – 2)/( b – 2)<BR>\n" );
document.write( "Over a common denominator of (b-2), we have<BR>\n" );
document.write( "b+2(b-2)=2b-2, cancelling out the denominator<BR>\n" );
document.write( "b+2b-4=2b-2<BR>\n" );
document.write( "b=2<BR>\n" );
document.write( "That root always has to be substituted into the original equation. <BR>\n" );
document.write( "Here, it causes a denominator to be 0 and is extraneous.  There is no solution to this equation.   When numbers are squared, when denominators may disappear in the algebra, in the end, the result obtained must be checked in the original equation.  A negative x cannot be a value for sqrt (x) in the original equation, and b=2 is not a root here. </SPAN>\n" );
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