To find the multiplicative inverse of a given expression, let's denote the expression [tex]\( 4c + 5 \)[/tex].
The multiplicative inverse of a number or an expression [tex]\( x \)[/tex] is a number or expression [tex]\( y \)[/tex] such that when [tex]\( x \)[/tex] is multiplied by [tex]\( y \)[/tex], the result is 1. In mathematical terms, the multiplicative inverse of [tex]\( x \)[/tex] is [tex]\( \frac{1}{x} \)[/tex].
Given the expression [tex]\( 4c + 5 \)[/tex], to find its multiplicative inverse, we need to find a value such that:
[tex]\[
(4c + 5) \cdot \text{(multiplicative inverse)} = 1
\][/tex]
This implies that the multiplicative inverse of [tex]\( 4c + 5 \)[/tex] is:
[tex]\[
\frac{1}{4c + 5}
\][/tex]
Thus, the correct answer is:
[tex]\[
\frac{1}{4c + 5}
\][/tex]
