What is the domain of (2x^2-7x-16)/((x+4)(x-4)(x-7)) ?

The domain of (2x^2-7x-16)/((x+4)(x-4)(x-7)) is x 7

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domain of (2x^2-7x-16)/((x+4)(x-4)(x-7))

domain

\frac{2 x ^{2} - 7 x - 16}{( x + 4 ) ( x - 4 ) ( x - 7 )}

x < - 4 or - 4 < x < 4 or 4 < x < 7 or x > 7

Interval Notation

(- \infty, - 4) \cup (- 4, 4) \cup (4, 7) \cup (7, \infty)

Solution steps

Find undefined (singularity) points:

x = - 4, x = 4, x = 7

The function domain

x < - 4 or - 4 < x < 4 or 4 < x < 7 or x > 7

y = \frac{8 x + 5}{2 - 5 x}

f (x) = \frac{3 ( x + 2 )}{4 ( x + 3 )}

f (x) = \frac{x - 1}{x ^{2} - 9 x + 18}

f (x) = \frac{3 x + 1}{4 x - 5}

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

What is the domain of (2x^2-7x-16)/((x+4)(x-4)(x-7)) ?
The domain of (2x^2-7x-16)/((x+4)(x-4)(x-7)) is x<-4\lor-4<x<4\lor 4<x<7\lor x>7