What is the domain of (x^2+3x)/(5x^2-1) ?

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

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domain of (x^2+3x)/(5x^2-1)

domain

\frac{x ^{2} + 3 x}{5 x ^{2} - 1}

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

Interval Notation

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

Solution steps

Find undefined (singularity) points:

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

The function domain

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

f (x) = \frac{2 x - 5}{3 x - 9}

y = - \frac{3}{5} x + 7

y = x^{3} - x

f (x) = \frac{( x ^{2} - 25 )}{x ^{2} - 4 x - 5}

f (x) = cos (x)

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