Final answer:
The given complex fraction (-2/-7÷4/-9) simplifies to 9/14 after multiplying the first fraction by the reciprocal of the second and then simplifying the result.
Step-by-step explanation:
To evaluate and simplify the given complex fraction (-2/-7÷4/-9), we follow the rules of division for fractions. we can rewrite the division as a multiplication by taking the reciprocal of the second fraction:
(-2/-7) ÷ (4/-9) = (-2/-7) × (-9/4)
Multiplying these two fractions, we get:
(-2 × -9) / (-7 × 4) = 18 / 28
Now, we simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2:
Therefore, the simplified form of the given complex fraction is 9/14.
Note that this answer is not among the options provided, so there seems to be an error in the question or the options given.