SOLUTION: Simplify the expression x-2 x+5 ----- - ----- x^2-9 x+4

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So we want to simplify...

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...

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...

Now we can multiply both expression out using FOIL method...

Now we simply combine like terms...remember to distribute the - symbol...


And put it in standard form...

This is simplified in the lowest terms.
I hope this helps...
Good Luck!