What is the domain of y=(x^2+6x)/(4x^3-23x^2-6x) ?

The domain of y=(x^2+6x)/(4x^3-23x^2-6x) is x 6

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domain of y=(x^2+6x)/(4x^3-23x^2-6x)

domain

y = \frac{x ^{2} + 6 x}{4 x ^{3} - 23 x ^{2} - 6 x}

x < - \frac{1}{4} or - \frac{1}{4} < x < 0 or 0 < x < 6 or x > 6

Interval Notation

(- \infty, - \frac{1}{4}) \cup (- \frac{1}{4}, 0) \cup (0, 6) \cup (6, \infty)

Solution steps

Find undefined (singularity) points:

x = 0, x = - \frac{1}{4}, x = 6

The function domain

x < - \frac{1}{4} or - \frac{1}{4} < x < 0 or 0 < x < 6 or x > 6

f (x) = t + 8 ln (t + 4)

y = 81 - x^{2}

y = \frac{- 9 x - 26}{x + 3}

3 - lo g_{3} (2 - x)

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

What is the domain of y=(x^2+6x)/(4x^3-23x^2-6x) ?
The domain of y=(x^2+6x)/(4x^3-23x^2-6x) is x<-1/4 \lor-1/4 <x<0\lor 0<x<6\lor x>6