What is the domain of y=(x^2+2x-3)/((x-1)(x^2-4)) ?

The domain of y=(x^2+2x-3)/((x-1)(x^2-4)) is x 2

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domain of y=(x^2+2x-3)/((x-1)(x^2-4))

domain

y = \frac{x ^{2} + 2 x - 3}{( x - 1 ) ( x ^{2} - 4 )}

x < - 2 or - 2 < x < 1 or 1 < x < 2 or x > 2

Interval Notation

(- \infty, - 2) \cup (- 2, 1) \cup (1, 2) \cup (2, \infty)

Solution steps

Find undefined (singularity) points:

x = 1, x = - 2, x = 2

The function domain

x < - 2 or - 2 < x < 1 or 1 < x < 2 or x > 2

f (x) = x^{9} - 6 x^{4} + 9

y = x 4 - x^{2}

\frac{3 x - 2}{x - 1}

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

What is the domain of y=(x^2+2x-3)/((x-1)(x^2-4)) ?
The domain of y=(x^2+2x-3)/((x-1)(x^2-4)) is x<-2\lor-2<x<1\lor 1<x<2\lor x>2