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

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

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

domain

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

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

Interval Notation

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

Solution steps

Find undefined (singularity) points:

x = 5, x = - 5

The function domain

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

x - 1 - 1

f (x) = 6 x + 2

\frac{8}{x - 3}

7 + 4 t + 5 (11 - 3 t)

f (x) = \frac{1}{2} cos (2 x - \frac{π}{3})

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