document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1140273>Question 1140273</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the values of a and b that make the following expression an identity:\r<BR>\n" );
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document.write( " (5x+31)/((x−5)(x+2)) = a/(x−5) − b/(x+2)  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #760766 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=760766\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Multiply everything by (x-5)(x+2)<BR>\n" );
document.write( "the left side is 5x+31<BR>\n" );
document.write( "the right side is a(x+2)-b(x-5)<BR>\n" );
document.write( "so ax+2a-bx+5b=5x+31<BR>\n" );
document.write( "x(a-b)+2a+5b=5x+31; set the x term=5 and the constant term=31<BR>\n" );
document.write( "a-b=5<BR>\n" );
document.write( "2a+5b=31<BR>\n" );
document.write( "5a-5b=25<BR>\n" );
document.write( "so 7a=56, a=8<BR>\n" );
document.write( "b=3<BR>\n" );
document.write( "(8, 3)\r<BR>\n" );
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document.write( "check with x=7<BR>\n" );
document.write( "66/(18)=(8/2)-3/9=3 2/3 checks<BR>\n" );
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