What is the domain of f(x)=(5x^2+7x-13)/(3x^2+5x-2) ?

The domain of f(x)=(5x^2+7x-13)/(3x^2+5x-2) is x 1/3

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domain of f(x)=(5x^2+7x-13)/(3x^2+5x-2)

domain

f (x) = \frac{5 x ^{2} + 7 x - 13}{3 x ^{2} + 5 x - 2}

x < - 2 or - 2 < x < \frac{1}{3} or x > \frac{1}{3}

Interval Notation

(- \infty, - 2) \cup (- 2, \frac{1}{3}) \cup (\frac{1}{3}, \infty)

Solution steps

Find undefined (singularity) points:

x = \frac{1}{3}, x = - 2

The function domain

x < - 2 or - 2 < x < \frac{1}{3} or x > \frac{1}{3}

What is the domain of f(x)=(5x^2+7x-13)/(3x^2+5x-2) ?
The domain of f(x)=(5x^2+7x-13)/(3x^2+5x-2) is x<-2\lor-2<x< 1/3 \lor x> 1/3