To find the quotient of the given expression:
[tex]\[
\frac{x^2-16}{x+4}
\][/tex]
we can follow these steps:
1. Factor the numerator: The numerator is [tex]\(x^2 - 16\)[/tex]. We recognize that this is a difference of squares, which can be factored using the identity [tex]\(a^2 - b^2 = (a - b)(a + b)\)[/tex].
Here, [tex]\(a = x\)[/tex] and [tex]\(b = 4\)[/tex], so:
[tex]\[
x^2 - 16 = (x - 4)(x + 4)
\][/tex]
2. Rewrite the expression: Substitute the factored form of the numerator back into the original expression:
[tex]\[
\frac{(x - 4)(x + 4)}{x + 4}
\][/tex]
3. Simplify the expression: Now, observe that the [tex]\(x + 4\)[/tex] term in the numerator and the denominator can be cancelled out (assuming [tex]\(x \neq -4\)[/tex] to avoid division by zero):
[tex]\[
\frac{(x - 4)\cancel{(x + 4)}}{\cancel{x + 4}} = x - 4
\][/tex]
Thus, the quotient of the expression is:
[tex]\[
x - 4
\][/tex]
Please enter the correct answer:
[tex]\[
x - 4
\][/tex]
