Where defined, which of the following is equivalent to (4-25x²)/(5x²-13x-6)?

Rationale

(4-25x²)/(5x²-13x-6) is equivalent to (2-5x)/(x-3).

To confirm this equivalence, we can perform polynomial long division or factorization on both the numerator and denominator. Upon simplification, we find that the expression indeed reduces to (2-5x)/(x-3).

A ((2-5x)/(x-3)) CORRECT

This choice directly represents the simplified form of the given expression. By factoring the numerator and denominator, we see that they share a common factor that simplifies the fraction correctly, validating this option as equivalent.

B ((5x-2)/(x-3)) YOUR ANSWER

This option presents an incorrect numerator. The numerator (5x-2) does not align with the original expression's numerator after simplification. Hence, it cannot be equivalent to (4-25x²)/(5x²-13x-6).

C ((2+5x)/(x-3)) YOUR ANSWER

This choice has an incorrect sign in the numerator. The term (2+5x) does not match the simplified form of the original expression, which should have a negative sign in front of the 5x, confirming that this option is not equivalent.

D ((2-5x)/(x+3)) YOUR ANSWER

While the numerator is correct, the denominator (x+3) does not match the simplified expression's denominator of (x-3). This discrepancy in the denominator indicates that this option is not equivalent to the original expression.

E ((5x-2)/(x+3)) YOUR ANSWER

Similar to option D, this choice has an incorrect numerator and denominator. The numerator (5x-2) does not match the correct form, and the denominator (x+3) also fails to correspond to the simplified expression, proving this option to be incorrect.

Conclusion

The expression (4-25x²)/(5x²-13x-6) simplifies to (2-5x)/(x-3). This is the only choice that maintains both the correct numerator and denominator after simplification. The other options present either incorrect numerators or denominators, confirming their ineffectiveness in representing the original expression. Thus, choice A stands as the valid equivalent expression.

Where defined, which of the following is equivalent to (4-25x²)/(5x²-13x-6)?

(4-25x²)/(5x²-13x-6) is equivalent to (2-5x)/(x-3).

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