What is the domain of sqrt(((x+4)(x+5))/(x-7)) ?

The domain of sqrt(((x+4)(x+5))/(x-7)) is -5 7

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domain of sqrt(((x+4)(x+5))/(x-7))

domain

\frac{( x + 4 ) ( x + 5 )}{x - 7}

- 5 \leq x \leq - 4 or x > 7

Interval Notation

[- 5, - 4] \cup (7, \infty)

Solution steps

Find non-negative values for radicals:

- 5 \leq x \leq - 4 or x > 7

Find undefined (singularity) points:

x = 7

Combine real regions and undefined points for final function domain

- 5 \leq x \leq - 4 or x > 7

What is the domain of sqrt(((x+4)(x+5))/(x-7)) ?
The domain of sqrt(((x+4)(x+5))/(x-7)) is -5<= x<=-4\lor x>7