Function Notations:

(f + g)(x) Means to add
equations

(f – g)(x) Means to subtract
equations

(f ●g)(x) Means to multiply
equations

(f/g)(x) Means to divide
equations

(f ᵒ g)(x) Or f(g(x)) – replace all x’s in the f(x)
equation with the equation g(x)-fog just means f of x

You should factor your
final answer. If x is replaced with a number, plug it into the equation.

Example one:
(f/g)(x)
2x+3/4x²-9

The denominator factors to (2x-3)(2x+3) and the (2x+3) cancels
out which leaves you with 1/2x-3.

Example two: (f-g)(x)
2x+3 - ( 4x²-9)

which foils to -4x²+2x+12, then you take a -1 which leaves you with
4x²-2x-12 l then you factors of 48 that subtract to give you -2 which is -8 and
6, 4x²-8x+6x-12, you then take out a 4x
and 6 which gives you 4x(x-2)+6(x-2). You
are then left with (4x+6)(x-2).