Question

find the domain of the rational function. express your answer in set builder notation.

1. $f(x)=\frac{x+1}{(x+3)(x-4)}$

$x\
eq -3\\ \\ x\
eq 4$

1. $\\{x|x$ is a real number $x\

eq -3,\\ x\
eq 4\\}$

1. $f(x)=\frac{x-7}{(x+4)(x-9)}$

$x\
eq -4\\ \\ x\
eq 9$

1. $\\{x|x$ is a real number $x\

eq -4,\\ x\
eq 9\\}$

1. $f(x)=\frac{3x}{(x+1)^2}$
2. _______

Explanation:

Step1: Identify denominator zero condition

Set $(x+1)^2 = 0$

Step2: Solve for x

$x+1=0 \implies x=-1$

Step3: Define domain (all reals except x=-1)

Domain is all real numbers where $x
eq -1$

Answer:

$\{x \mid x \text{ is a real number}, x
eq -1\}$