Question

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

Answer 1

Answer:x=-3 nonextraneous

Step-by-step explanation:

Answer 2

Answer:

Non-extraneous x = −3

Step-by-step explanation:

Here, the given expression is,

$\frac{6}{x-3}=\frac{3}{x}$

$\implies 6x = 3(x-3)$   ( By the cross multiplication ),

$\implies 6x = 3x - 9$

$\implies 6x - 3x = -9$

$\implies 3x = -9$

$\implies x = -3$

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 $\frac{6}{x-3}=\frac{3}{x}$ follows,

⇒ x = -3 is the non-extraneous,

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