The largest negative integer for which \[\dfrac{(x-4)\cdot (x-2)}{(x-1)\cdot (x-5)}>0\] is
A.-2
B.-1
C.-3
D.-4

Hint: -An integer is a whole number (not a fractional number) that can be positive, negative, or zero.
Examples of integers are: -5, 1, 5, 8, 97, and 3,043.
Examples of numbers that are not integers are: -1.43, 1, 3.14, 0.09, and 5,643.1.

Complete step-by-step answer:
The set of integers, denoted Z, is formally defined as follows:
Z = {..., -3, -2, -1, 0, 1, 2, 3 ...}
For a fraction to be positive either both the numerator should be positive or both of them should be negative.

As mentioned in the hint, we have to find the value of the largest negative number that will give a positive value of the expression that is given.
Now, as mentioned in the hint, we can see that as all the options that are given are negative and none of them can give a positive value, both the numerator and the denominator have to be negative.
Now, for the numerator and the denominator to be negative, we can put any value from the options, so, the largest negative integer for which the expression will be positive is -1.

Note: -The students can make an error if they don’t know how to assess the question.
Another way of doing this question is by directly putting the options at the place of x and then evaluating the expression to check whether it is positive or negative.