Answer: Option (b) is the correct answer.
Step-by-step explanation:
A solution that is obtained from the process of solving the problem but is not a defined or valid solution for the problem is known as an extraneous solution.
The given equation is as follows.
[tex]\frac{3}{x-3} = \frac{x}{x-3}- \frac{3}{2}[/tex]
Solving this equation as follows.
[tex]\frac{3}{x-3} = \frac{x}{x-3}- \frac{3}{2}[/tex]
Taking L.C.D on the right side as 2(x - 3), then the equation will be as follows.
[tex]\frac{3}{x-3} = \frac{x(2)-3(x-3)}{2(x-3)}[/tex]
[tex]\frac{3}{x-3} = \frac{2x-3x+9}{2(x-3)}[/tex]
[tex]\frac{3}{x-3} = \frac{(-x+9)}{2(x-3)}[/tex]
Cancelling (x-3) from both the sides, the equation will be as follows.
[tex]3 = \frac{(-x+9)}{2}[/tex]
-x + 9 = 6
x = 3
Therefore, x = 3 and when we put x = 3 into the given equation then it becomes undefined. As a result, the value which makes a given equation undefined is also known as extraneous.
Thus, we can conclude that out of the given options x = 3, extraneous is the correct answer.
