Question

Which domain restrictions apply to rational expression? x2+5x+6x2−9 Select each correct answer.

x≠−1

x≠1

x≠2

x≠3

x≠−3

x≠−2

Answer 1

The domain restrictions apply to rational expression are:

$x\neq 3\\\\x\neq -3$

Solution:

Given rational expression is:

$\frac{x^2 + 5x + 6}{x^2 - 9}$

We have to find the domain restrictions apply to rational expression

From given,

$\frac{x^2 + 5x + 6}{x^2 - 9}$

Use the identity,

$a^2 - b^2 = (a+b)(a-b)$

Therefore,

$\frac{x^2 + 5x + 6}{(x+3)(x-3)}$

The rational expression is undefined when denominator is 0

From above, see the denominator (x + 3) and (x - 3)

When x = -3 and x = 3, the denominator becomes 0

Thus, domain restrictions are:

$x\neq 3\\\\x\neq -3$