Question

Finding the domain of a rational function. F(x)=x/x^2-4

Answer 1

If the equation is x/(x^2-4) then I will solve it here

it's rational
therefor we can't have any impossibles like dividing by zero and square root of -1 an d stuff



f(x)=x/(x^2-4)

we know that the denomenator cannot be equal to zero so the numbers you cannot user are the numbers that will make the bottom number zero
so x^2-4=0
x^2=4
x=-2 or 2

so x cannot be -2 or 2, but it can be all other numbers so
domain=all numbers except -2 and 2

Answer 2

$f(x)=\frac{x}{x^2-4}\\\\D:x^2-4\neq2\ \ \ \ |add\ 4\ to \both\ sides\\\\x^2\neq4\iff x\neq\pm\sqrt4\Rightarrow x\neq-2\ and\ x\neq2\\\\Answer:\boxed{Domain\ D:x\in\mathbb{R}-\{-2;\ 2\}}$