document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=136648>Question 136648</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0395977223/algebrahomeworkh>Algebra Structure and Method</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> The numerator of a fraction is 1 less than the denominator.  If the numerator and the denominator are both increased by 4, the new fraction will be 1/8 more than the original fraction.  Find the original fraction. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #100087 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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/cgi-bin/show-face.mpl?user=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=100087\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The numerator of a fraction is 1 less than the denominator.  If the numerator and the denominator are both increased by 4, the new fraction will be 1/8 more than the original fraction.  Find the original fraction.<BR>\n" );
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document.write( "Write an equation for what it says:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F%28%28x%2B1%29%29 ALIGN=MIDDLE  ALT=\"x%2F%28%28x%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F8 ALIGN=MIDDLE  ALT=\"1%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%2B4%29%29%2F%28%28x%2B1%2B4%29%29 ALIGN=MIDDLE  ALT=\"%28%28x%2B4%29%29%2F%28%28x%2B1%2B4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F%28%28x%2B1%29%29 ALIGN=MIDDLE  ALT=\"x%2F%28%28x%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F8 ALIGN=MIDDLE  ALT=\"1%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%2B4%29%29%2F%28%28x%2B5%29%29 ALIGN=MIDDLE  ALT=\"%28%28x%2B4%29%29%2F%28%28x%2B5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The common denominator will be 8(x+1)(x+5)<BR>\n" );
document.write( "Multiply each term by this, cancel out the denominators, leaving us with:<BR>\n" );
document.write( "x(8(x+5) + (x+1)(x+5) = 8(x+4)(x+1)<BR>\n" );
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document.write( "8x^2 + 40x + x^2 + 6x + 5 = 8(x^2 + 5x + 4)<BR>\n" );
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document.write( "8x^2 + 40x + x^2 + 6x + 5 = 8x^2 + 40x + 32<BR>\n" );
document.write( "Combine on the left:<BR>\n" );
document.write( "8x^2 + x^2 - 8x^2 + 40x + 6x - 40x + 5 - 32 = 0<BR>\n" );
document.write( "A quadratic equation<BR>\n" );
document.write( "x^2 + 6x - 27 = 0<BR>\n" );
document.write( "Factors to:<BR>\n" );
document.write( "(x+9)(x-3) = 0<BR>\n" );
document.write( "We want the positive solution:<BR>\n" );
document.write( "x = 3<BR>\n" );
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document.write( "Check solution in original equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F%28%284%29%29 ALIGN=MIDDLE  ALT=\"3%2F%28%284%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F8 ALIGN=MIDDLE  ALT=\"1%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%287%29%29%2F%28%288%29%29 ALIGN=MIDDLE  ALT=\"%28%287%29%29%2F%28%288%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Actually the negative solution x = -9 will work also:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-9%29%2F%28%28-8%29%29 ALIGN=MIDDLE  ALT=\"%28-9%29%2F%28%28-8%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F8 ALIGN=MIDDLE  ALT=\"1%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28-5%29%29%2F%28%28-5%29%29 ALIGN=MIDDLE  ALT=\"%28%28-5%29%29%2F%28%28-5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Did I make this understandable? Any questions? </SPAN>\n" );
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