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

The domain of (x^3+5x^2)/(7x^2-2) is x sqrt(2/7)

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

domain

\frac{x ^{3} + 5 x ^{2}}{7 x ^{2} - 2}

x < - \frac{2}{7} or - \frac{2}{7} < x < \frac{2}{7} or x > \frac{2}{7}

Interval Notation

(- \infty, - \frac{2}{7}) \cup (- \frac{2}{7}, \frac{2}{7}) \cup (\frac{2}{7}, \infty)

Solution steps

Find undefined (singularity) points:

x = \frac{2}{7}, x = - \frac{2}{7}

The function domain

x < - \frac{2}{7} or - \frac{2}{7} < x < \frac{2}{7} or x > \frac{2}{7}

f (x) = \frac{2}{( \frac{2}{x - 7} ) - 7}

f (x) = \frac{x}{2 x - ∣ x ∣}

f (x) = x^{2} + 8 x - 9

f (x) = \frac{6 x}{x ^{2} - 14 x + 45}

(x - 9) (x^{2} - 18 x - 162)

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