Question

If $a$ is greater than $4$, then, of the following, which will always have the least value?

• A. $\frac{4}{a-1}$
• B. $\frac{4}{a}$
• C. $\frac{4}{a+1}$
• D. $\frac{a}{4}$
• E. $\frac{a+1}{4}$

Answer 1

The correct option is C $\frac{4}{a+1}$

$a>4$

so $\frac{a}{4}>1$.........1

$\frac{4}{a}<1$...............2

$\frac{a+1}{4}>\frac{a}{4}$.........3

$\frac{4}{a+1}<\frac{4}{a}$..........4

by 1,2,3,4 we can say

$\frac{4}{a+1}<\frac{4}{a}<1<\frac{a}{4}<\frac{a+1}{4}$

so $\frac{4}{a+1}$ is least.