What is the domain of f(x)=(x+6)/((x-7)(x+5)) ?

The domain of f(x)=(x+6)/((x-7)(x+5)) is x 7

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domain of f(x)=(x+6)/((x-7)(x+5))

domain

f (x) = \frac{x + 6}{( x - 7 ) ( x + 5 )}

x < - 5 or - 5 < x < 7 or x > 7

Interval Notation

(- \infty, - 5) \cup (- 5, 7) \cup (7, \infty)

Solution steps

Find undefined (singularity) points:

x = 7, x = - 5

The function domain

x < - 5 or - 5 < x < 7 or x > 7

What is the domain of f(x)=(x+6)/((x-7)(x+5)) ?
The domain of f(x)=(x+6)/((x-7)(x+5)) is x<-5\lor-5<x<7\lor x>7