What is the domain of (-2x^2+5x+3)/(4x^2-9) ?

The domain of (-2x^2+5x+3)/(4x^2-9) is x 3/2

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domain of (-2x^2+5x+3)/(4x^2-9)

domain

\frac{- 2 x ^{2} + 5 x + 3}{4 x ^{2} - 9}

x < - \frac{3}{2} or - \frac{3}{2} < x < \frac{3}{2} or x > \frac{3}{2}

Interval Notation

(- \infty, - \frac{3}{2}) \cup (- \frac{3}{2}, \frac{3}{2}) \cup (\frac{3}{2}, \infty)

Solution steps

Find undefined (singularity) points:

x = \frac{3}{2}, x = - \frac{3}{2}

The function domain

x < - \frac{3}{2} or - \frac{3}{2} < x < \frac{3}{2} or x > \frac{3}{2}

f (x) = \frac{x}{x ^{2} + 14 x + 45}

f (x) = 2 - \frac{12}{x + 5}, - 7 \leq x \leq 7

lo g_{10} (2) (x - 2)

f (x) = x^{2} - x - 1

1 + sin (x)

What is the domain of (-2x^2+5x+3)/(4x^2-9) ?
The domain of (-2x^2+5x+3)/(4x^2-9) is x<-3/2 \lor-3/2 <x< 3/2 \lor x> 3/2