Question 39242
So we want to simplify...
{{{(x-2)/(x^2-9) - (x+5)/(x+4)}}}
First, when adding or subtracting fractions we need to find the lowest common denominator (LCD).
To make it simple we can just combine the two existing deniminators, like so...
(x^2-9)(x+4)
This is you LCD.
We can now multiply each expression by the LCD...
So now the equation looks like this...
{{{(x^2-9)(x+4)*(x-2)/(x^2-9) - (x+5)/(x+4)*(x^2-9)(x+4)}}}
Now we can cancel the like terms in each expression to eliminate the denominator and the fraction...
In the first expression the (x^2-9) cancels out
and in the second expression the (x+4) cancels out.
So now we have...
{{{(x+4)(x-2) - (x+5)(x^2-9)}}}
Now we can multiply both expression out using FOIL method...
{{{(x^2+4x-2x-8)-(x^3-9x+5x-45)}}} 
Now we simply combine like terms...remember to distribute the - symbol...
{{{x^2+2x-8-x^3+9x-5x+45}}}
{{{x^2+2x-8-x^3+4x+45}}}
And put it in standard form...
{{{x^3+x^2+6x+37}}}
This is simplified in the lowest terms.
I hope this helps...
Good Luck!