2) x = 3 is not included in the domain
3) x = 2 and x = -2 are not included in the domain
Explanation:
To get the domain of a function, the denominator is equated to zero.
The value of x not included in the domain will make the equation undefined if we substitute it into the given equation
[tex]\begin{gathered} 2)\text{ }\frac{3}{x-3}\text{ = }\frac{x}{x-3}-\frac{x}{4} \\ factors:\text{ \lparen x - 3\rparen } \\ \left(x\text{ - 3\rparen occurred twice, we only need one to find the doamin}\right? \\ LCD:\text{ x - 3 = 0} \\ x\text{ = 3 \lparen is the value of x not included in the domain\rparen} \end{gathered}[/tex][tex]\begin{gathered} 3)\text{ }\frac{1}{x\text{ + 2}}\text{ + }\frac{1}{x\text{ - 2}}\text{ = }\frac{4}{x^2-4} \\ factors:\text{ \lparen x +2\rparen and \lparen x-2\rparen} \\ LCD:\text{ \lparen x+2\rparen\lparen x-2\rparen = 0} \\ x\text{ + 2 = 0} \\ \text{x = -2} \\ x\text{ - 2 = 0} \\ x\text{ = 2} \\ x\text{ = -2 and x = 2 are values of x not included in the domain} \end{gathered}[/tex]
