document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=947573>Question 947573</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1/(x-4) + 1/(x+2) = 8/7<BR>\n" );
document.write( "find x<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #578226 by </B><A HREF=/tutors/aboutme.mpl?userid=addingup><B>addingup(3677)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=addingup><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=addingup><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=578226\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's bring the two together with the common denominator (x-4)(x+2):\r<BR>\n" );
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document.write( "2(x-1)/(x-4)(x+2)= 8/7. Cross multiply to clear the fractions:\r<BR>\n" );
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document.write( "14(x-1)= 8(x-4)(x+2)Expand out the terms on both sides:\r<BR>\n" );
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document.write( "14x-14= 8x^2-16x-64 Subtract 8x^2-16x-64 from both sides, and you get:\r<BR>\n" );
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document.write( "-8x^2+30x+50= 0 Factor the left hand side:\r<BR>\n" );
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document.write( "-2(x-5)(4x+5)=0 Divide both sides by -2:\r<BR>\n" );
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document.write( "(x-5)(4x+5)=0 Split into 2 equations:\r<BR>\n" );
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document.write( "x-5= 0 or 4x+5=0 On the left add 5 and on the left subtract 5, both sides:\r<BR>\n" );
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document.write( "x=5 or 4x= -5 Solve for x on the right, divide both sides by 4, and\r<BR>\n" );
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document.write( "Solution: x=5 or x= -5/4 which you can also write as -1 1/4<BR>\n" );
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