document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=277318>Question 277318</A>: <I><SPAN STYLE=\"word-break: break-all;\"> My son has 2 problems that seem impossible.\r<BR>\n" );
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document.write( "(1) 1/(x-1)-(2(3x+1)/5x-2)+1/(1-x)=0\r<BR>\n" );
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document.write( "(2)(7x+5)/6-(5(x-1))/4=1/3+8/(1-x)\r<BR>\n" );
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document.write( "Thank you for your help </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #201946 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=201946\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Thank you for your prompt reply.  We are still not sure how in problem 1 you can modify the equation 1/(x-1)...+ 1/(1-x)to your modification of 1/(x-1)...- 1/(x-1).  <BR>\n" );
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document.write( "(1) <BR>\n" );
document.write( "1/(x-1)-(2(3x+1)/5x-2)+1/(1-x)=0 <BR>\n" );
document.write( "Modify the 3rd term: +1/(1-x) <BR>\n" );
document.write( "Multiply numerator and denominator by -1 to get -1/(x-1)<BR>\n" );
document.write( "Also apply the distributive law on the 2nd term.\r<BR>\n" );
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document.write( "[1/(x-1)] - [(6x+2)/(5x-2)] - [(1/(x-1)] = 0<BR>\n" );
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document.write( "Notice that the 1st and 3rd terms add up to zero.<BR>\n" );
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document.write( "(6x+2)/(5x-2) = 0<BR>\n" );
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document.write( "The fraction will be zero when the numerator is zero:<BR>\n" );
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document.write( "6x+2 = 0<BR>\n" );
document.write( "6x = -2<BR>\n" );
document.write( "x = -2/6<BR>\n" );
document.write( "x = -1/3<BR>\n" );
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document.write( "The same question arises in problem 2 when you go from ... 1/3 + 8/(1-x) to ...1/3 - 8/(x-1).  Perhaps you can explain that.<BR>\n" );
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document.write( "you have 8/(1-x)<BR>\n" );
document.write( "Multiply numerator and denominator by -1 to get:<BR>\n" );
document.write( "-8/(x-1)\r<BR>\n" );
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document.write( "(2)<BR>\n" );
document.write( "[(7x+5)/6]-[(5(x-1))/4] = [1/3]+[8/(1-x)]\r<BR>\n" );
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document.write( "---<BR>\n" );
document.write( "[(7x+5)/6]-[(5(x-1))/4] = [1/3]-[8/(x-1)]<BR>\n" );
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document.write( "Multiply thru by 12(x-1) to get rid of the denominators:<BR>\n" );
document.write( "[2(x-1)(7x+5)] - [15(x-1)^2] = [4(x-1)] - [12*8]<BR>\n" );
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document.write( "Modify:<BR>\n" );
document.write( "[2(7x^2-2x-5] - [15(x^2-2x+1)] = [4x-4]-[96]<BR>\n" );
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document.write( "14x^2-4x-10-15x^2+30x-15 = 4x-100<BR>\n" );
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document.write( "-x^2+26x-15 = 4x-100<BR>\n" );
document.write( "-x^2+22x+85 = 0<BR>\n" );
document.write( "x^2-22x-85 = 0<BR>\n" );
document.write( "Factor:<BR>\n" );
document.write( "(x-17)(x-5) = 0<BR>\n" );
document.write( "x = 17 or x = 5<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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document.write( " </SPAN>\n" );
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