What is the domain of (3x^2+8x+4)/(3x^2-4x-4) ?

The domain of (3x^2+8x+4)/(3x^2-4x-4) is x 2

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domain of (3x^2+8x+4)/(3x^2-4x-4)

domain

x < - \frac{2}{3} or - \frac{2}{3} < x < 2 or x > 2

Interval Notation

(- \infty, - \frac{2}{3}) \cup (- \frac{2}{3}, 2) \cup (2, \infty)

Solution steps

Find undefined (singularity) points:

x = 2, x = - \frac{2}{3}

The function domain

x < - \frac{2}{3} or - \frac{2}{3} < x < 2 or x > 2

What is the domain of (3x^2+8x+4)/(3x^2-4x-4) ?
The domain of (3x^2+8x+4)/(3x^2-4x-4) is x<-2/3 \lor-2/3 <x<2\lor x>2