Question
Mathematics Question on Inequalities
If x is a positive number, then which of the following fractions has the greatest value?
A
xx
B
xx+1
C
(x+1)x
D
(x+3)(x+2)
Answer
xx+1
Explanation
Solution
The correct option is (B): xx+1
Explanation: The given options are:
- xx=1
- xx+1=1+x1
- x+1x
- x+3x+2
Since x is a positive number, let's compare the values of these fractions:
- xx=1
- xx+1=1+x1, which is always greater than 1.
- x+1x, which is always less than 1 for any positive x.
- x+3x+2, which is also less than 1 for any positive x.
Clearly, xx+1 has the greatest value because it is always greater than 1, while the other fractions are less than or equal to 1.
Thus, the correct answer is B: xx+1.