Answer:
[tex]T\text{he domain of H\lparen x\rparen is }\lbrace x\lvert x-3,1\rbrace[/tex]
Step-by-step explanation:
The domain of a function is all the set of possible x-values that the function can take. Then, for the given function:
[tex]H\left(x\right)=\frac{-7x^2}{\left(x-1\right)\left(x+3\right)}[/tex]
The function is undefined when the denominator is equal to 0, then equalize each factor of the denominator to 0:
[tex]\begin{gathered} x-1=0 \\ x=1 \\ \\ x+3=0 \\ x=-3 \\ \\ \text{ Then, the domain of H\lparen x\rparen is }\lbrace x\lvert x\ne-3,1\rbrace \end{gathered}[/tex]
