What is the domain of (sqrt(x+5))/(3x^2+10x+3) ?

The domain of (sqrt(x+5))/(3x^2+10x+3) is -5 -1/3

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domain of (sqrt(x+5))/(3x^2+10x+3)

domain

\frac{x + 5}{3 x ^{2} + 10 x + 3}

- 5 \leq x < - 3 or - 3 < x < - \frac{1}{3} or x > - \frac{1}{3}

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x \geq - 5

Find undefined (singularity) points:

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

Combine real regions and undefined points for final function domain

- 5 \leq x < - 3 or - 3 < x < - \frac{1}{3} or x > - \frac{1}{3}

\frac{( x - 1 )}{x + 2}

lo g_{10} (2 ((x - 1)) + 1)

f (x) = \frac{1}{4 x + 1}

4 x^{2} + 8 x + 3

f (x) = \frac{arctan ( x )}{x ^{2} - 1}

What is the domain of (sqrt(x+5))/(3x^2+10x+3) ?
The domain of (sqrt(x+5))/(3x^2+10x+3) is -5<= x<-3\lor-3<x<-1/3 \lor x>-1/3