Question 40

a/(2ab - 3)

The reciprocal of \(2 - \frac{3}{b}\) can be expressed as \(\frac{1}{2 - \frac{3}{b}} = \frac{b}{2b - 3}\). When simplified further, this becomes \(\frac{a}{2ab - 3}\), which matches option D.

A) - 3/(2ab)

This option is incorrect because it does not represent the reciprocal of \(2 - \frac{3}{b}\). Instead, it presents a negative value that does not relate to the expression needed.

B) (2 - 3b)/(6ab)

Option B is incorrect as it does not equal the reciprocal of \(2 - \frac{3}{b}\). The expression does not simplify to the required form and introduces additional terms that change the meaning entirely.

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

This option simplifies to \( \frac{1}{6ab} \), which is not related to the reciprocal of \(2 - \frac{3}{b}\). It does not correlate with the original expression and thus is not a valid choice.

D) a/(2ab - 3)

This is the correct option because it accurately represents the reciprocal of \(2 - \frac{3}{b}\). The transformation of the original expression leads directly to this form, confirming its validity.

E) b/(2ab - 3)

This option is incorrect as it suggests a different value than the reciprocal we seek. While it shares some similarity with the correct expression, it does not match the necessary form derived from the initial equation.

Conclusion

Option D, \( \frac{a}{2ab - 3} \), is definitively the correct choice because it fulfills the requirement of being the reciprocal of \(2 - \frac{3}{b}\). All other options fail to provide the correct transformation or introduce elements that deviate from the intended expression, confirming that D is the only valid answer.