document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=304676>Question 304676</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need to solve a rational equation that simplifies to a quadratic equation:<BR>\n" );
document.write( "(z+7)/(z+3)=(z+1)/(z+7)+1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #218196 by </B><A HREF=/tutors/aboutme.mpl?userid=dabanfield><B>dabanfield(803)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=dabanfield><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=218196\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (z+7)/(z+3)=(z+1)/(z+7)+1\r<BR>\n" );
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document.write( "(z+7)/(z+3) - (z+1)/(z+7) = 1\r<BR>\n" );
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document.write( "A common denominator for the left side is (z+3)*(z+7). So we multiply the first term by (z+7)/(z+7) = 1 and the second term by (z+3)/(z+3) = 1 gives us:\r<BR>\n" );
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document.write( "(z+7)*(z+7)/(z+3)*(z+7) - (z+1)*(z+3)/(z+7)*(z+3) = 1\r<BR>\n" );
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document.write( "((z+7)^2 - (z+1)*(z+3))/((z+3)*(z+7)) = 1\r<BR>\n" );
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document.write( "(z^2 + 14z + 49 - (z^2 + 4z + 3))/(z^2 + 10z + 21) = 1<BR>\n" );
document.write( "(10z + 46)/(z^2 + 10z + 21) = 1<BR>\n" );
document.write( "Multiply both sides by z^2 + 10z + 21:<BR>\n" );
document.write( "10z + 46 = z^2 + 10z + 21<BR>\n" );
document.write( "z^2 - 25 = 0<BR>\n" );
document.write( "(z+5)*(z-5) = 0\r<BR>\n" );
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document.write( "z = -5 or z = 5\r<BR>\n" );
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document.write( " </SPAN>\n" );
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