Question

Solve 3 over x minus 3 equals the quantity of x over x minus 3, minus three-halves for x and determine if the solution is extraneous or not. x = 3, non-extraneous x = 3, extraneous x = -3, extraneous x = -3, non-extraneous

Answer 1

Answer: Option (b) is the correct answer.

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.

`(3)/(x-3) = (x)/(x-3)- (3)/(2)`

Solving this equation as follows.

`(3)/(x-3) = (x)/(x-3)- (3)/(2)`

Taking L.C.D on the right side as 2(x - 3), then the equation will be as follows.

`(3)/(x-3) = (x(2)-3(x-3))/(2(x-3))`

`(3)/(x-3) = (2x-3x+9)/(2(x-3))`

`(3)/(x-3) = ((-x+9))/(2(x-3))`

Cancelling (x-3) from both the sides, the equation will be as follows.

`3 = ((-x+9))/(2)`

-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.

Answer 2

multiply both sides by 2(x-3)

6=2x−3x2+9x,3x2−11x+6=0

3x^2-9x-2x+6=0
3x(x-3)-2(x-3)=0
(x-3)(3x-2)=0 x−3=0 or x=3 is an extraneous root. or 3x-2=0 calculate x.