Question 1001695
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You need to determine where the function under the logarithm, 


f(x) = {{{(x^2-9)/(x^2 + 9x + 14)}}}  is greater than zero,  f(x) > 0.


Notice that  1)  {{{x^2-9)=}}} = (x+3)*(x-3),  and  2)  {{{x^2 + 9x + 14}}} = (x+2)*(x+7).     Therefore, 


f(x) = {{{((x+3)*(x-3))/((x+7)*(x+2))}}}.


Now,  f(x) > 0 


1) &nbsp;in the semi-infinite interval &nbsp;x < -7, &nbsp;or &nbsp;({{{-infinity}}}, {{{-7}}});


2) &nbsp;in the interval &nbsp;-3 < x < -2, &nbsp;or &nbsp;(-3, -2);


3) &nbsp;in the semi-infinite interval &nbsp;x > 3, &nbsp;or &nbsp;({{{3}}}, {{{infinity}}}).


See the plots below.


<TABLE> 
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  <TD> 

{{{graph( 330, 330, -12.5, 6.5, -11.5, 8.5,
           (x^2-9)/(x^2 + 9x + 14),
           x^2 -9, x^2 + 9x + 14
)}}}


<B>Figure</B>. Plot f(x) (red line);
plot of the numerator (green line);
plot of denominator (blue line).

  </TD>
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</TABLE>