1. Factor the denomiator and numerator if possible.
For the first fraction, we can factor out the gcf of the denomiator.
[tex] \frac{x + 1}{3(x + 6)} [/tex]
For the second fraction, we can use FOIL Method to factor.
which gives us
[tex] - \frac{x - 5}{(x + 6)(x - 4)} [/tex]
So we know have
[tex] \frac{x + 1}{3(x + 6)} - \frac{x - 5}{(x + 6)(x - 4)} [/tex]
2. We must make the denomaitor the same. Since they already start a (x-6) term we don't need to multiply that
First, multiply 3 to the second fraction.
[tex] \frac{x + 1}{3(x + 6)} - \frac{3(x - 5)}{3(x + 6)(x - 4)} [/tex]
Then, we multiply the first fraction by (x-4).
[tex] \frac{(x + 1)(x - 4)}{3(x + 6)(x - 4)} - \frac{3(x - 5)}{3(x + 6)(x - 4)} [/tex]
3. Simplify the numerator.
[tex] \frac{ {x}^{2} + 5x + 4}{3(x + 6)(x - 4)} - \frac{3x - 15}{3(x + 6)(x - 4)} [/tex]
[tex] \frac{ {x}^{2} + 2x + 19 }{3(x + 6)(x - 4)} [/tex]
