document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=992166>Question 992166</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me out with this math.<BR>\n" );
document.write( "The numerator of a fraction is 5 less than its denominator. If 6 is added to the numerator and 4 to the denominator,the fraction is double. What is the fraction? </SPAN>\n" );
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document.write( "The numerator of a fraction is 5 less than its denominator. If 6 is added to the numerator and 4 to the denominator, the fraction is double. What is the fraction?<BR>\n" );
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document.write( "Let &nbsp;x&nbsp; be the numerator of the fraction.<BR>\n" );
document.write( "Then the denominator is &nbsp;(x+5), &nbsp;according to the first condition, and the fraction is &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F%28x%2B5%29 ALIGN=MIDDLE  ALT=\"x%2F%28x%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "According to the second condition, &nbsp;you have an equation \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B6%29%2F%28%28x%2B5%29%2B4%29 ALIGN=MIDDLE  ALT=\"%28x%2B6%29%2F%28%28x%2B5%29%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A%28x%2F%28x%2B5%29%29 ALIGN=MIDDLE  ALT=\"2%2A%28x%2F%28x%2B5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Simplify and solve it:\r<BR>\n" );
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document.write( "(x+6)*(x+5) = 2x*(x+9),\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+6x+%2B+5x+%2B+30 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+6x+%2B+5x+%2B+30\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2+%2B+18x ALIGN=MIDDLE  ALT=\"2x%5E2+%2B+18x\"   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=x%5E2+%2B+7x+-+30 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+7x+-+30\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This equation has the roots &nbsp;x = 3 &nbsp;and &nbsp;x = -10.\r<BR>\n" );
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document.write( "Thus the fractions are &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F%283%2B5%29 ALIGN=MIDDLE  ALT=\"3%2F%283%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F8 ALIGN=MIDDLE  ALT=\"3%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > &nbsp;and &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-10%29%2F%28-10%2B5%29 ALIGN=MIDDLE  ALT=\"%28-10%29%2F%28-10%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-2%29%2F1 ALIGN=MIDDLE  ALT=\"%28-2%29%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The second number does not satisfies the problem condition, while the first does.\r<BR>\n" );
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document.write( "But be careful !!!\r<BR>\n" );
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document.write( "The fraction &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F8 ALIGN=MIDDLE  ALT=\"3%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > &nbsp;satisfies the condition.\r<BR>\n" );
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document.write( "The fraction &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2F16 ALIGN=MIDDLE  ALT=\"6%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" >&nbsp; is the same number, &nbsp;but do not satisfies the condition. &nbsp;So, this problem is, &nbsp;actually, &nbsp;a danger play with words. \r<BR>\n" );
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