Answer
C
Step-by-step explanation:
[tex]\frac{w^2-9}{w^2-4w-21}[/tex] ( factorise numerator and denominator )
w^2 - 9 ← is a difference of squares and factors as
w² - 9 = (w - 3)(w + 3)
w² - 4w - 21
Consider the factors of the constant term (- 21) which sum to give the coefficient of the w- term ( - 4)
The factors are - 7 and + 3 , since
- 7 × + 3 = - 21 and - 7 + 3 = - 4 , then
w² - 4w - 21 = (w - 7)(w + 3)
Then
[tex]\frac{(w-3)(w+3)}{(w-7)(w+3)}[/tex] ← cancel the common factor (w + 3) on numerator/ denominator
= [tex]\frac{w-3}{w-7}[/tex] → C
