document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=997722>Question 997722</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello friends can someone equate the coefficients on this problem  8/y^3-4y . I tried to  equate the coefficients but it does not work. Please show equating the coefficients!!! Do not solve by plugging in clever values if it is possible!!!  I know how to solve it by plugging in clever values. Thank you in advance!!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #615694 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=615694\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i did a little research and i think i understand the process.\r<BR>\n" );
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document.write( "start with 8 / (y^3 - 4y)\r<BR>\n" );
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document.write( "factor the denominator to get:\r<BR>\n" );
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document.write( "8 / (y * (y+2) * (y-2))\r<BR>\n" );
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document.write( "i believe they call it that you decompose the fraction to get:\r<BR>\n" );
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document.write( "8 / (y * (y+2) * (y-2)) = A/y + B/(y+2) + C/(y-2)\r<BR>\n" );
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document.write( "you now multiply both sides of this eqaution by (y * (y+2) * (y-2) to get rid of the fractions.\r<BR>\n" );
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document.write( "you are left with:\r<BR>\n" );
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document.write( "8 = A*(y+2)*(y-2) + B*y*(y-2) + C*y*(y+2)\r<BR>\n" );
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document.write( "you now simplify the right side of the equation to get:\r<BR>\n" );
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document.write( "8 = A*(y^2-4) + B*(y^2-2y) + C*(y^2+2y)\r<BR>\n" );
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document.write( "you now simplify the right side further by performing the operations indicated to get:\r<BR>\n" );
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document.write( "8 = A*y^2 - 4a + B*y^2 - 2By + C*y^2 + 2Cy\r<BR>\n" );
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document.write( "you now combine like terms and reorder the terms in descending order to get:\r<BR>\n" );
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document.write( "8 = A*y^2 + B*y^2 + C*y^2 - 2By + 2Cy - 4A\r<BR>\n" );
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document.write( "you now factor out the common terms to get:\r<BR>\n" );
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document.write( "8 = (A + B + C)*y^2 + (-2B + 2C)*y - 4A.\r<BR>\n" );
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document.write( "you now take your expression on the left and add in the missing terms to get:\r<BR>\n" );
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document.write( "8 = 0*y^2 + 0*y + 8\r<BR>\n" );
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document.write( "your equation becomes:\r<BR>\n" );
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document.write( "0*y^2 + 0*y + 8 = (A + B + C)*y^2 + (-2B + 2C)*y - 4A.\r<BR>\n" );
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document.write( "you now equate the coefficients from the right side of the equation and the left side of the equation for the terms with the same variables.\r<BR>\n" );
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document.write( "A+B+C = 0 for the y^2 term.<BR>\n" );
document.write( "-2B + 2C = 0 for the y term.<BR>\n" );
document.write( "-4A = 8 for the constant term.\r<BR>\n" );
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document.write( "-4A = 8 leads to A = -2\r<BR>\n" );
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document.write( "-2B + 2C = 0 leads to B = C\r<BR>\n" );
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document.write( "A+B+C = 0 becomes -2 + B + C = 0\r<BR>\n" );
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document.write( "since B = C, this becomes either -2 + 2B = 0, or -2 + 2C = 0\r<BR>\n" );
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document.write( "either way, you get B = 1 and C = 1\r<BR>\n" );
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document.write( "you are left with:<BR>\n" );
document.write( "A = -2<BR>\n" );
document.write( "B = 1<BR>\n" );
document.write( "C = 1\r<BR>\n" );
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document.write( "your solution is:\r<BR>\n" );
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document.write( "8 / (y^3 - 4y) = -2/y + 1/(y+2) + 1/(y-2)\r<BR>\n" );
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document.write( "you can confirm the solution is correct by picking any number to be equal to y and then seeing if the equation is true.\r<BR>\n" );
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document.write( "i picked y = 17 \r<BR>\n" );
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document.write( "i got:\r<BR>\n" );
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document.write( "8 / (y^3 - 4y) = -2/y + 1/(y+2) + 1/(y-2) becomes:\r<BR>\n" );
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document.write( "8 / (17^3 - 4*17) = -2/17 + 1/19 + 1/15\r<BR>\n" );
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document.write( "this was resolved to get:\r<BR>\n" );
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document.write( ".0016511868 = .0016511868\r<BR>\n" );
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document.write( "since they are the same, this confirmed the solution is correct.\r<BR>\n" );
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document.write( "here's a reference from the web you might find useful.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://www.youtube.com/watch?v=7cgOf3alK40\" target = \"_blank\">https://www.youtube.com/watch?v=7cgOf3alK40</a>\r<BR>\n" );
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document.write( "patrickJMT has numerous examples you can look at if you want to dive into it further, including examples where the denominator doesn't factor.\r<BR>\n" );
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document.write( "there are also numerous other youtube videos that talk about the same subject.\r<BR>\n" );
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document.write( "this is about as far as i want to go into it so good luck with the rest.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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