document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=97394>Question 97394</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Resolve 7-8x/(1-x)*(2-x)into partial fractions.Hence find the expansion of the function in ascending powers of x as far as three nonzero terms. State for which values of x this expansion is valid\r<BR>\n" );
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document.write( "I need this answer,today.Please. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #70875 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=70875\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287-8x%29%2F%28%281-x%29%282-x%29%29 ALIGN=MIDDLE  ALT=\"%287-8x%29%2F%28%281-x%29%282-x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287-8x%29%2F%28%281-x%29%282-x%29%29=A%2F%281-x%29%2BB%2F%282-x%29 ALIGN=MIDDLE  ALT=\"%287-8x%29%2F%28%281-x%29%282-x%29%29=A%2F%281-x%29%2BB%2F%282-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the fraction into two smaller fractions\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281-x%29%282-x%29%28%287-8x%29%2F%28%281-x%29%282-x%29%29%29=%281-x%29%282-x%29%28A%2F%281-x%29%2BB%2F%282-x%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by the LCD <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281-x%29%282-x%29 ALIGN=MIDDLE  ALT=\"%281-x%29%282-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This will eliminate any fractions. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%28%281-x%29%282-x%29%29%28%287-8x%29%2F%28cross%28%281-x%29%282-x%29%29%29%29=A%2Across%28%281-x%29%29%282-x%29%2Fcross%28%281-x%29%29%2BB%281-x%29%2Across%28%282-x%29%29%2Fcross%28%282-x%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute. Notice the denominators cancel.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7-8x=A%282-x%29%2BB%281-x%29 ALIGN=MIDDLE  ALT=\"7-8x=A%282-x%29%2BB%281-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify\r<BR>\n" );
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document.write( "Now to find A, simply eliminate B. So to eliminate B, let x=1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7-8%281%29=A%282-1%29%2BB%281-1%29 ALIGN=MIDDLE  ALT=\"7-8%281%29=A%282-1%29%2BB%281-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > plug in x=1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7-8=A%282-1%29%2BB%281-1%29 ALIGN=MIDDLE  ALT=\"7-8=A%282-1%29%2BB%281-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1=A%281%29%2BB%280%29 ALIGN=MIDDLE  ALT=\"-1=A%281%29%2BB%280%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1=A ALIGN=MIDDLE  ALT=\"-1=A\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply \r<BR>\n" );
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document.write( "So our first value is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=-1 ALIGN=MIDDLE  ALT=\"A=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now to find B, simply eliminate A. So to eliminate A, let x=2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7-8%282%29=A%282-2%29%2BB%281-2%29 ALIGN=MIDDLE  ALT=\"7-8%282%29=A%282-2%29%2BB%281-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > plug in x=2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7-16=A%282-2%29%2BB%281-2%29 ALIGN=MIDDLE  ALT=\"7-16=A%282-2%29%2BB%281-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-9=A%280%29%2BB%28-1%29 ALIGN=MIDDLE  ALT=\"-9=A%280%29%2BB%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-9=-B ALIGN=MIDDLE  ALT=\"-9=-B\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply and combine like terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9=B ALIGN=MIDDLE  ALT=\"9=B\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by -1\r<BR>\n" );
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document.write( "So our second value is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=9 ALIGN=MIDDLE  ALT=\"B=9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So our values are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=-1 ALIGN=MIDDLE  ALT=\"A=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=9 ALIGN=MIDDLE  ALT=\"B=9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So that means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287-8x%29%2F%28%281-x%29%282-x%29%29=-1%2F%281-x%29%2B9%2F%282-x%29 ALIGN=MIDDLE  ALT=\"%287-8x%29%2F%28%281-x%29%282-x%29%29=-1%2F%281-x%29%2B9%2F%282-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C%3E1 ALIGN=MIDDLE  ALT=\"x%3C%3E1\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C%3E2 ALIGN=MIDDLE  ALT=\"x%3C%3E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Check: \r<BR>\n" );
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document.write( "To verify the answer, simply compare the graphs of the original expression and the answer. You'll see that they are equivalent, so that verifies your answer. </SPAN>\n" );
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