Question

Simplify the expression

Answer 1

Notice that we have a difference of squares in the numerator of our expression. In the denominator we have a quadratic expression of the form $ax^2+bx+c$. So we can factor both numerator and denominator and cancel common terms:
$\frac{w^2-9}{w^2-4w-21}= \frac{w^2-3^2}{(w+3)(w-7)} = \frac{(w+3)(w-3)}{(w+3)(w-7)}= \frac{w-3}{w-7}$

We can conclude that the correct answer is the fourth one: $\frac{w-3}{w-7}$