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 [tex]ax^2+bx+c[/tex]. So we can factor both numerator and denominator and cancel common terms:
[tex] \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} [/tex]
We can conclude that the correct answer is the fourth one: [tex]\frac{w-3}{w-7}[/tex]
