Question 51

x = 2

To satisfy the equation 2/(x - 2) = 0, the denominator must not be zero, but the fraction itself must approach zero. Since 2 divided by any non-zero number cannot equal zero, the only point where the expression is undefined is when x is 2.

A) 1

Choosing x = 1 gives 2/(1 - 2) = 2/(-1) = -2, which is not equal to zero. Therefore, this option is incorrect.

B) 2

If x = 2, the expression 2/(2 - 2) is undefined because the denominator becomes zero. However, since the original equation cannot equal zero, this option is the only point where the expression does not have a defined value and is the critical point to consider.

C) 4

Substituting x = 4 results in 2/(4 - 2) = 2/2 = 1, which does not satisfy the equation as it does not equal zero. Thus, this option is also incorrect.

D) 5

If x = 5, then 2/(5 - 2) = 2/3, which is not equal to zero. Therefore, this option is incorrect.

E) 10

Choosing x = 10 gives 2/(10 - 2) = 2/8 = 1/4, which again does not equal zero. Hence, this option is incorrect as well.

Conclusion

The correct answer is x = 2, which is the point where the expression becomes undefined, highlighting the nature of the equation. All other options yield values that do not satisfy the original equation, confirming that option B is the only correct choice.