document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=381369>Question 381369</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write the partial fraction decomposition of the following rational expression.\r<BR>\n" );
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document.write( "(x^2-x-8)/(x+1)(x^2+5x+6)\r<BR>\n" );
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document.write( "For this type of problem, how can I check if my answer is correct?\r<BR>\n" );
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document.write( "Here is how I solved the problem:<BR>\n" );
document.write( "First, I factored the denominator.<BR>\n" );
document.write( "(x^2-x-8)/(x+1)(x+3)(x+2)\r<BR>\n" );
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document.write( "Then, (A)/(x+1) + (B)/(x+3) + (C)/(x+2)<BR>\n" );
document.write( "Multiplied all by LCD to get rid of fractions, left with: (x^2-x-8)=A(x+3)(x+2)+B(x+1)(x+2)+C(x+3)(x+1)\r<BR>\n" );
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document.write( "Solved for A first by letting x=-1, that way B and C drop out.<BR>\n" );
document.write( "A=-3\r<BR>\n" );
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document.write( "Solved for B by letting x=-3 so A and C drop out.<BR>\n" );
document.write( "B=2\r<BR>\n" );
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document.write( "Solved for C by letting x=-2 so A and B drop out.<BR>\n" );
document.write( "C=2\r<BR>\n" );
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document.write( "I plug in A, B, and C back into this (A)/(x+1) + (B)/(x+3) + (C)/(x+2) and my final answer is:\r<BR>\n" );
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document.write( "((-3)/(x+1))+((2)/(x+3))+((2)/(x+2))\r<BR>\n" );
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document.write( "Is this correct? Also, how can I verify in the future if my answer is correct if for example I have to do a similar problem on an exam? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #270505 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=270505\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You have the correct answer (and the correct steps). Good job.\r<BR>\n" );
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document.write( "You can verify the answer by graphing each side of the equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2-x-8%29%2F%28%28x%2B1%29%28x%5E2%2B5x%2B6%29%29=-3%2F%28x%2B1%29%29%2B2%2F%28x%2B3%29%29%2B2%2F%28x%2B2%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "as two separate equations\r<BR>\n" );
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document.write( "In other words, set the left side equal to y to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28x%5E2-x-8%29%2F%28%28x%2B1%29%28x%5E2%2B5x%2B6%29%29 ALIGN=MIDDLE  ALT=\"y=%28x%5E2-x-8%29%2F%28%28x%2B1%29%28x%5E2%2B5x%2B6%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and graph that. Then graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-3%2F%28x%2B1%29%29%2B2%2F%28x%2B3%29%29%2B2%2F%28x%2B2%29%29 ALIGN=MIDDLE  ALT=\"y=-3%2F%28x%2B1%29%29%2B2%2F%28x%2B3%29%29%2B2%2F%28x%2B2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (the right side)\r<BR>\n" );
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document.write( "You'll then find that the two graphs match up (ie one graph is right on top of the other), which confirms that they are equal. You can even compare the table of values for each equation and you'll find that the two tables are identical.\r<BR>\n" );
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document.write( "If you need more help, email me at <a  rel=nofollow HREF=\"mailto:jim_thompson5910@hotmail.com?Subject=Algebra%20Help\">jim_thompson5910@hotmail.com</a>\r<BR>\n" );
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document.write( "Also, feel free to check out my <a  rel=nofollow HREF=\"http://www.freewebs.com/jimthompson5910/home.html\">tutoring website</a>\r<BR>\n" );
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document.write( "Jim </SPAN>\n" );
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