If 2a – 3/b ≠ 0, which of the following equals the reciprocal of 2a - 3/b?

Rationale

a/(2ab - 3)

To find the reciprocal of (2a - frac{3}{b}), we first rewrite the expression as a single fraction: ( frac{2ab - 3}{b} ). The reciprocal of this expression is obtained by flipping the numerator and denominator, resulting in ( frac{b}{2ab - 3} ).

A (- 3/(2ab)) YOUR ANSWER

This choice does not represent the reciprocal of (2a - frac{3}{b}). Instead, it appears to be a fraction that simplifies the original expression incorrectly, omitting the necessary components to maintain equality.

B ((2 - 3ab)/(6ab)) YOUR ANSWER

This option is also incorrect as it does not reflect the reciprocal of the original expression. Instead, it represents a completely different algebraic manipulation that does not simplify to the reciprocal form needed.

C ((3 - 2ab)/(6ab)) YOUR ANSWER

This choice is incorrect as well. It does not correspond to the reciprocal of (2a - frac{3}{b}) and misrepresents the relationships between the variables involved.

D (a/(2ab - 3)) CORRECT

This choice correctly identifies the reciprocal of (2a - frac{3}{b}). The original expression can be rewritten as ( frac{2ab - 3}{b} ), and taking the reciprocal gives us ( frac{b}{2ab - 3} ), which means the answer can also be expressed in terms of (a) as ( frac{a}{2ab - 3} ).

E (b/(2ab - 3)) YOUR ANSWER

While this choice closely resembles the correct reciprocal, it mistakenly presents (b) as the numerator instead of (a). This crucial distinction renders it incorrect.

Conclusion

The reciprocal of the expression (2a - frac{3}{b}) simplifies to ( frac{b}{2ab - 3} ) and can be expressed equivalently as ( frac{a}{2ab - 3} ) when considering the proper formulation. Therefore, choice D accurately represents the reciprocal, while the others fail to maintain the integrity of the original expression's mathematical relationship.

If 2a – 3/b ≠ 0, which of the following equals the reciprocal of 2a - 3/b?

a/(2ab - 3)

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