What is the domain of ((5-2x)sqrt(2x+3))/(2+x) ?

The domain of ((5-2x)sqrt(2x+3))/(2+x) is x>=-3/2

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domain of ((5-2x)sqrt(2x+3))/(2+x)

domain

\frac{( 5 - 2 x ) 2 x + 3}{2 + x}

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

Interval Notation

[- \frac{3}{2}, \infty)

Solution steps

Find non-negative values for radicals:

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

Find undefined (singularity) points:

x = - 2

Combine real regions and undefined points for final function domain

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

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

2 x - 9

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

f (x) = \frac{5 x + 14}{6 x ^{2} + x - 2}

f (x) = \frac{x + 9}{x ^{2} - 49}

What is the domain of ((5-2x)sqrt(2x+3))/(2+x) ?
The domain of ((5-2x)sqrt(2x+3))/(2+x) is x>=-3/2