Question

simplify: $\frac{x^2-16}{x-4}$
what does the given expression simplify to?
$(x + 4)$
what is the excluded value of $x$ for the given expression?
-16
-14
0
4

Explanation:

Step1: Factor the numerator

The numerator $x^2 - 16$ is a difference of squares, so it factors to $(x-4)(x+4)$.
Expression: $x^2 - 16 = (x-4)(x+4)$

Step2: Cancel common factors

Cancel the $(x-4)$ term in numerator and denominator (valid when $x
eq 4$).
Expression: $\frac{(x-4)(x+4)}{x-4} = x+4$

Step3: Find excluded value

Excluded values make the denominator zero. Set $x-4=0$ and solve for $x$.
Expression: $x-4=0 \implies x=4$

Answer:

1. The simplified expression is $x+4$
2. The excluded value is $\boldsymbol{4}$ (from the dropdown options)