What is the domain of f(x)=(3x^2-3)/(2x^2+7x+5) ?

The domain of f(x)=(3x^2-3)/(2x^2+7x+5) is x -1

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domain of f(x)=(3x^2-3)/(2x^2+7x+5)

domain

f (x) = \frac{3 x ^{2} - 3}{2 x ^{2} + 7 x + 5}

x < - \frac{5}{2} or - \frac{5}{2} < x < - 1 or x > - 1

Interval Notation

(- \infty, - \frac{5}{2}) \cup (- \frac{5}{2}, - 1) \cup (- 1, \infty)

Solution steps

Find undefined (singularity) points:

x = - 1, x = - \frac{5}{2}

The function domain

x < - \frac{5}{2} or - \frac{5}{2} < x < - 1 or x > - 1

f (x) = 3 x^{2} - 130 x + 1000

(- 2, - 8), (- 10, - 2)

f (x) = (x - 11)^{2}, x \leq 11

f (x) = \frac{( 3 x + 1 )}{( x - 2 )}

f (x) = x^{3} - x^{2} + x - 1

What is the domain of f(x)=(3x^2-3)/(2x^2+7x+5) ?
The domain of f(x)=(3x^2-3)/(2x^2+7x+5) is x<-5/2 \lor-5/2 <x<-1\lor x>-1