What is the domain of f(x)=(-18t^2+54t)/(t^2+7t+10) ?

The domain of f(x)=(-18t^2+54t)/(t^2+7t+10) is t -2

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domain of f(x)=(-18t^2+54t)/(t^2+7t+10)

domain

f (x) = \frac{- 18 t ^{2} + 54 t}{t ^{2} + 7 t + 10}

t < - 5 or - 5 < t < - 2 or t > - 2

Interval Notation

(- \infty, - 5) \cup (- 5, - 2) \cup (- 2, \infty)

Solution steps

Find undefined (singularity) points:

t = - 2, t = - 5

The function domain

t < - 5 or - 5 < t < - 2 or t > - 2

f (x) = \frac{x - 10}{2}

\frac{x - 1}{2 x + 9}

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

5 x^{2} + 2 x - 1

5 x^{2} + 2 x - 8

What is the domain of f(x)=(-18t^2+54t)/(t^2+7t+10) ?
The domain of f(x)=(-18t^2+54t)/(t^2+7t+10) is t<-5\lor-5<t<-2\lor t>-2