The domain is the set of all real number except 1 and -1
Explanation:
We have the following function:
[tex]f(x)=\frac{3x}{4x^2-4}[/tex]
So the domain is the set of all x-values for which the function is defined. Since we have [tex]4x^2-4[/tex] in the denominator, then:
[tex]4x^2-4\neq 0 \\ \\ \\ Factor \ out \ 4: \\ \\ 4(x^2-1)\neq 0 \\ \\ (x^2-1)\neq 0 \\ \\ \\ Difference \ of \ squares: \\ \\ (x-1)(x+1)\neq 0 \\ \\ \\ So: \\ \\ \\\boxed{x\neq 1 \ and \ x\neq -1}[/tex]
In conclusion:
The domain is the set of all real number except 1 and -1
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