document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209068>Question 1209068</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve 3a + 4b = 5a - 6b + 24 + a/(b^3 - 7b + 24) for a in terms of b. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #847824 by </B><A HREF=/tutors/aboutme.mpl?userid=yurtman><B>yurtman(42)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=yurtman><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=847824\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To solve for `a`, we'll first group the terms involving `a` on one side of the equation:\r<BR>\n" );
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document.write( "```<BR>\n" );
document.write( "3a + 4b = 5a - 6b + 24 + a/(b^3 - 7b + 24)<BR>\n" );
document.write( "3a - 5a - a/(b^3 - 7b + 24) = 24 - 6b - 4b<BR>\n" );
document.write( "```\r<BR>\n" );
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document.write( "Combine like terms:\r<BR>\n" );
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document.write( "```<BR>\n" );
document.write( "-3a - a/(b^3 - 7b + 24) = 24 - 10b<BR>\n" );
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document.write( "Factor out `a` on the left side:\r<BR>\n" );
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document.write( "```<BR>\n" );
document.write( "a(-3 - 1/(b^3 - 7b + 24)) = 24 - 10b<BR>\n" );
document.write( "```\r<BR>\n" );
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document.write( "To isolate `a`, divide both sides by the factor `(-3 - 1/(b^3 - 7b + 24))`:\r<BR>\n" );
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document.write( "```<BR>\n" );
document.write( "a = (24 - 10b) / (-3 - 1/(b^3 - 7b + 24))<BR>\n" );
document.write( "```\r<BR>\n" );
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document.write( "To simplify the complex fraction, we can multiply the numerator and denominator by `(b^3 - 7b + 24)`:\r<BR>\n" );
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document.write( "```<BR>\n" );
document.write( "a = [(24 - 10b)(b^3 - 7b + 24)] / [(-3)(b^3 - 7b + 24) - 1]<BR>\n" );
document.write( "```\r<BR>\n" );
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document.write( "Expanding the numerator and simplifying the denominator:\r<BR>\n" );
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document.write( "```<BR>\n" );
document.write( "a = (24b^3 - 168b + 576 - 10b^4 + 70b^2 - 240b) / (-3b^3 + 21b - 72 - 1)<BR>\n" );
document.write( "```\r<BR>\n" );
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document.write( "Combining like terms:\r<BR>\n" );
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document.write( "```<BR>\n" );
document.write( "a = (-10b^4 + 24b^3 + 70b^2 - 408b + 576) / (-3b^3 + 21b - 73)<BR>\n" );
document.write( "```\r<BR>\n" );
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document.write( "So, the solution for `a` in terms of `b` is:\r<BR>\n" );
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document.write( "```<BR>\n" );
document.write( "a = (-10b^4 + 24b^3 + 70b^2 - 408b + 576) / (-3b^3 + 21b - 73)<BR>\n" );
document.write( "```<BR>\n" );
document.write( " </SPAN>\n" );
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