What is the domain of f(x)=(x^2+5x+6)/(x^2+2x-8) ?

The domain of f(x)=(x^2+5x+6)/(x^2+2x-8) is x 2

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domain of f(x)=(x^2+5x+6)/(x^2+2x-8)

domain

f (x) = \frac{x ^{2} + 5 x + 6}{x ^{2} + 2 x - 8}

x < - 4 or - 4 < x < 2 or x > 2

Interval Notation

(- \infty, - 4) \cup (- 4, 2) \cup (2, \infty)

Solution steps

Find undefined (singularity) points:

x = 2, x = - 4

The function domain

x < - 4 or - 4 < x < 2 or x > 2

f (x) = \frac{1}{x + 5} - \frac{1}{x - 5} = 0

\frac{5}{\frac{11}{x} + 2}

x^{3} - 3 x^{2} + 7 x + 1

f (x) = - \frac{4}{1 + x ^{2}}

f (x) = 5 x + 5

What is the domain of f(x)=(x^2+5x+6)/(x^2+2x-8) ?
The domain of f(x)=(x^2+5x+6)/(x^2+2x-8) is x<-4\lor-4<x<2\lor x>2