Your verbal description of the expression you're dealing with is a bit unclear, but here's what I'm assuming you're given:
[tex]\frac{2}{x^2-9} - \frac{3x}{x^2+5x+6}[/tex]
To subtract two fractions, you need a common denominator. To find out what that should be, factor the two denominators.
[tex]\frac{2}{(x+3)(x-3)} - \frac{3x}{(x+2)(x+3)}[/tex]
The least common denominator (LCD) must contain each distinct factor, so the LCD is [tex](x+3)(x-3)(x+2)[/tex]
Now change the two fractions so they have the LCD. In this case, that means to multiply top & bottom of the first fraction by the "missing" factor (x + 2) and the second fraction's top & bottom by (x - 3).
[tex]\frac{2(x+3)}{(x+3)(x-3)(x+2)} - \frac{3x(x-3)}{(x+3)(x-3)(x+2)}[/tex]
Now, distribute the 2 in the first numerator and 3x in the second numerator (careful with that subtraction sign!) and simplify.
[tex]\frac{2x+4}{(x+3)(x-3)(x+2)}-\frac{3x^2-9x}{(x+3)(x-3)(x+2)}[/tex]
Can you finish it?
