Question

Solve 6 over x minus 3 equals 3 over x for x and determine if the solution is extraneous or not

Answer 1

Here, the given expression is,

( By the cross multiplication ),

Since, an extraneous solution is a solution, which is emerged by solving the equation but it does not satisfying the equation,

But for x = -3, the equation follows,

⇒ x = -3 is the non-extraneous,

⇒ The given equation has only one solution x = -3 which is non-extraneous.

Explanation:

Answer 2

x = -3 is not extraneous solution.

Explanation:

`(6)/(x-3) =(3)/(x)\\Cross\,\, Multiply\\6x =3(x-3)\\6x = 3x-9\\6x-3x=-9\\3x= -9\\x=-9/3\\x=-3`

An extraneous solution is the solution that is obtained by solving the question given but does not satisfy the original equation.

In our case x = -3

Putting value back to the original equation

`(6)/(x-3) =(3)/(x)\\(6)/(-3-3) =(3)/(-3)\\(6)/(-6) =-1\\-1=-1`

Since our original equation is satisfied so,

x = -3 is not extraneous solution.