What is the domain of f(x)=(x^2+5x+6)/(x^2-3x-10) ?

The domain of f(x)=(x^2+5x+6)/(x^2-3x-10) is x 5

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domain of f(x)=(x^2+5x+6)/(x^2-3x-10)

domain

f (x) = \frac{x ^{2} + 5 x + 6}{x ^{2} - 3 x - 10}

x < - 2 or - 2 < x < 5 or x > 5

Interval Notation

(- \infty, - 2) \cup (- 2, 5) \cup (5, \infty)

Solution steps

Find undefined (singularity) points:

x = 5, x = - 2

The function domain

x < - 2 or - 2 < x < 5 or x > 5

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

y = 2 x + 3, (1, 5)

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

\frac{3 x}{7 x - 1}

5 x + 3

What is the domain of f(x)=(x^2+5x+6)/(x^2-3x-10) ?
The domain of f(x)=(x^2+5x+6)/(x^2-3x-10) is x<-2\lor-2<x<5\lor x>5