document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1043622>Question 1043622</A>: <I><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%28x%2B1%29%2Bb%28x-1%29%29%2F%28x-2%29=2%2B%281%2F%28x-2%29%29 ALIGN=MIDDLE  ALT=\"%28a%28x%2B1%29%2Bb%28x-1%29%29%2F%28x-2%29=2%2B%281%2F%28x-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The equation above is true for all values of x&#8800;2, where a and b are constats. What is the value of a?<BR>\n" );
document.write( "A) -1/2<BR>\n" );
document.write( "B) 2<BR>\n" );
document.write( "C) 3<BR>\n" );
document.write( "D) 4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #658771 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=658771\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 2 + ( 1 / (x-2) ) = (2x-3) / (x-2), then<BR>\n" );
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document.write( "a(x+1) + b(x-1) = 2x-3<BR>\n" );
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document.write( "ax+a +bx-b = 2x-3<BR>\n" );
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document.write( "we have two equations in 2 unknowns<BR>\n" );
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document.write( "1) ax +bx = 2x<BR>\n" );
document.write( "2) a -b = -3<BR>\n" );
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document.write( "solve 2) for b<BR>\n" );
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document.write( "b = a +3<BR>\n" );
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document.write( "substitute for b in equation 1)<BR>\n" );
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document.write( "ax +(a+3)x = 2x<BR>\n" );
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document.write( "2ax = -x<BR>\n" );
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document.write( "a = -0.5<BR>\n" );
document.write( "answer is A)<BR>\n" );
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document.write( "check our answer<BR>\n" );
document.write( "a = -0.5, then b = -0.5 +3 = 2.5<BR>\n" );
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document.write( "substitute for a and b in the original equation<BR>\n" );
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document.write( "(-0.5(x+1) + 2.5(x-1)) / (x-2) =<BR>\n" );
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document.write( "(-0.5x -0.5 +2.5x -2.5) / (x-2) =<BR>\n" );
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document.write( "(2x - 3) / (x-2) = 2 + ( 1 / (x-2) ) = (2x -3) / (x-2)<BR>\n" );
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document.write( "our answer checks  :-)<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );