document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1201042>Question 1201042</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write each rational expression as an equivalent expression with the indicated denominator.\r<BR>\n" );
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document.write( "\frac{14}{z^2-3z}=\frac{?}{z\left(z-3\right)\left(z-2\right)} </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #835294 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3816)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=835294\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "LHS = left hand side<BR>\n" );
document.write( "RHS = right hand side\r<BR>\n" );
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document.write( "Let n be the unknown numerator expression in the RHS fraction.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14%2F%28z%5E2-3z%29+=+n%2F%28z%28z-3%29%28z-2%29%29 ALIGN=MIDDLE  ALT=\"14%2F%28z%5E2-3z%29+=+n%2F%28z%28z-3%29%28z-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "n is some expression in terms of z.\r<BR>\n" );
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document.write( "Let's factor the denominator of the LHS.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E2-3z+=+z%28z-3%29 ALIGN=MIDDLE  ALT=\"z%5E2-3z+=+z%28z-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This means<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14%2F%28z%5E2-3z%29+=+n%2F%28z%28z-3%29%28z-2%29%29 ALIGN=MIDDLE  ALT=\"14%2F%28z%5E2-3z%29+=+n%2F%28z%28z-3%29%28z-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "is the same as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14%2F%28z%28z-3%29%29+=+n%2F%28z%28z-3%29%28z-2%29%29 ALIGN=MIDDLE  ALT=\"14%2F%28z%28z-3%29%29+=+n%2F%28z%28z-3%29%28z-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The factors for the LHS denominator are z and (z-3). Both of which are present in the RHS denominator <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%28z-3%29%28z-2%29 ALIGN=MIDDLE  ALT=\"z%28z-3%29%28z-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. The LHS denominator is missing the factor (z-2).\r<BR>\n" );
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document.write( "We'll multiply top and bottom of the LHS fraction by (z-2) to fill in that missing gap.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14%2F%28z%28z-3%29%29+=+n%2F%28z%28z-3%29%28z-2%29%29 ALIGN=MIDDLE  ALT=\"14%2F%28z%28z-3%29%29+=+n%2F%28z%28z-3%29%28z-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2814%2Ahighlight%28%28z-2%29%29%29%2F%28z%28z-3%29%2Ahighlight%28%28z-2%29%29%29+=+n%2F%28z%28z-3%29%28z-2%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2814%2A%28z-2%29%29%2F%28z%28z-3%29%2A%28z-2%29%29+=+n%2F%28z%28z-3%29%28z-2%29%29 ALIGN=MIDDLE  ALT=\"%2814%2A%28z-2%29%29%2F%28z%28z-3%29%2A%28z-2%29%29+=+n%2F%28z%28z-3%29%28z-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2814z-14%2A2%29%2F%28z%28z-3%29%28z-2%29%29+=+n%2F%28z%28z-3%29%28z-2%29%29 ALIGN=MIDDLE  ALT=\"%2814z-14%2A2%29%2F%28z%28z-3%29%28z-2%29%29+=+n%2F%28z%28z-3%29%28z-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2814z-28%29%2F%28z%28z-3%29%28z-2%29%29+=+n%2F%28z%28z-3%29%28z-2%29%29 ALIGN=MIDDLE  ALT=\"%2814z-28%29%2F%28z%28z-3%29%28z-2%29%29+=+n%2F%28z%28z-3%29%28z-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Both denominators of the LHS and RHS have the same exact factorization. The fractions are only equal if the numerators were the same. Therefore, we must have n = 14(z-2) = 14z-28\r<BR>\n" );
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document.write( "In other words,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14%2F%28z%5E2-3z%29+=+%2814z-28%29%2F%28z%28z-3%29%28z-2%29%29 ALIGN=MIDDLE  ALT=\"14%2F%28z%5E2-3z%29+=+%2814z-28%29%2F%28z%28z-3%29%28z-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "after multiplying top and bottom by (z-2).<BR>\n" );
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