document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=537580>Question 537580</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am having the hardest time with this. Solve by the method of your choice:\r<BR>\n" );
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document.write( "(1/x^2-3x+2)=(1/x+2)+(5/x^2-4)\r<BR>\n" );
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document.write( "I have tried this different ways and just cant figure it out. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #352920 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=352920\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Although you wrote (according to the rules of algebra) that you were given to solve:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2Fx%5E2-3x%2B2%29=%281%2Fx%2B2%29%2B%285%2Fx%5E2-4%29 ALIGN=MIDDLE  ALT=\"%281%2Fx%5E2-3x%2B2%29=%281%2Fx%2B2%29%2B%285%2Fx%5E2-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "I'm guessing that you really were to solve the following:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F%28x%5E2-3x%2B2%29%29=%281%2F%28x%2B2%29%29%2B%285%2F%28x%5E2-4%29%29 ALIGN=MIDDLE  ALT=\"%281%2F%28x%5E2-3x%2B2%29%29=%281%2F%28x%2B2%29%29%2B%285%2F%28x%5E2-4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "If I'm wrong I apologize, and please ignore the following and re-submit your problem.<BR>\n" );
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document.write( "Start with:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F%28x%5E2-3x%2B2%29%29=%281%2F%28x%2B2%29%29%2B%285%2F%28x%5E2-4%29%29 ALIGN=MIDDLE  ALT=\"%281%2F%28x%5E2-3x%2B2%29%29=%281%2F%28x%2B2%29%29%2B%285%2F%28x%5E2-4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Where it is possible, factor the denominators. This will give you:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F%28%28x-2%29%2A%28x-1%29%29%29=%281%2F%28x%2B2%29%29%2B%285%2F%28%28x-2%29%2A%28x%2B2%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Next, multiply both sides (all terms) by the three factors common to the denominator. Just multiply each of the terms on both sides by:<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29%28x%2B2%29%28x-2%29 ALIGN=MIDDLE  ALT=\"%28x-1%29%28x%2B2%29%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "When you do that the equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28%28x-1%29%28x%2B2%29%28x-2%29%2A1%29%2F%28%28x-2%29%2A%28x-1%29%29%29=%28%28%28x-1%29%28x%2B2%29%28x-2%29%2A1%29%2F%28x%2B2%29%29%2B%28%28%28x-1%29%28x%2B2%29%28x-2%29%2A5%29%2F%28%28x-2%29%2A%28x%2B2%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now in each term cancel any factors that are in both the numerator and the denominator:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28cross%28%28x-1%29%29%28x%2B2%29cross%28%28x-2%29%29%2A1%29%2F%28cross%28%28x-2%29%29%2Across%28%28x-1%29%29%29%29=%28%28%28x-1%29cross%28%28x%2B2%29%29%28x-2%29%2A1%29%2Fcross%28%28x%2B2%29%29%29%2B%28%28%28x-1%29cross%28%28x%2B2%29%29cross%28%28x-2%29%29%2A5%29%2F%28cross%28%28x-2%29%29%2Across%28%28x%2B2%29%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and you are left with:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29+=+%28x-1%29%28x-2%29%2B+5%28x-1%29 ALIGN=MIDDLE  ALT=\"%28x%2B2%29+=+%28x-1%29%28x-2%29%2B+5%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Multiply out the two terms on the right side to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2+=+x%5E2-3x+%2B2%2B5x+-+5 ALIGN=MIDDLE  ALT=\"x%2B2+=+x%5E2-3x+%2B2%2B5x+-+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "On the right side combine the -3x and +5x to get +2x. Also combine the +2 and the -5 to get -3. This reduces the equation to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2+=+x%5E2+%2B2x+-3 ALIGN=MIDDLE  ALT=\"x%2B2+=+x%5E2+%2B2x+-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Then get everything on one side of the equation by subtracting x + 2 from both sides. The equation then becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+x%5E2+%2Bx+-5 ALIGN=MIDDLE  ALT=\"0+=+x%5E2+%2Bx+-5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Transpose it to the standard quadratic form:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2Bx-5+=0 ALIGN=MIDDLE  ALT=\"x%5E2+%2Bx-5+=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Solve by using the quadratic formula:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Recall that a is the multiplier of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Therefore, a = 1. b is the multiplier of the x. Therefore b also = 1. And c is the constant. And so c = -5. Substituting these values into the quadratic formula results in:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%28%2B1%29+%2B-+sqrt%28+1%5E2-4%2A1%2A%28-5%29+%29%29%2F%282%2A1%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-%28%2B1%29+%2B-+sqrt%28+1%5E2-4%2A1%2A%28-5%29+%29%29%2F%282%2A1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-1+%2B-+sqrt%28+1%5E2%2B20+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%28-1+%2B-+sqrt%28+1%5E2%2B20+%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So the two answers for x are:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-1+%2B+sqrt%28+21+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%28-1+%2B+sqrt%28+21+%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-1+-+sqrt%28+21+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%28-1+-+sqrt%28+21+%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Hope this helps you to clear up the places you had trouble with. <BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );