Question

Finding the domain of a rational function.

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

Answer 1

`f(x)=(x)/(x^2-4)\\\\D:x^2-4\\eq2\ \ \ \ |add\ 4\ to \both\ sides\\\\x^2\\eq4\iff x\\eq\pm\sqrt4\Rightarrow x\\eq-2\ and\ x\\eq2\\\\Answer:\boxed{Domain\ D:x\in\mathbb{R}-\{-2;\ 2\}}`

Answer 2

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