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

Question

asked Mar 7, 2017 196k views

2 Answers

Takashi Matsuo · Answer 1 · 2017-03-12T13:36:58+0000

Answer:

Non-extraneous x = −3

Explanation:

Here, the given expression is,

(6)/(x-3)=(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
(6)/(x-3)=(3)/(x) follows,

⇒ x = -3 is the non-extraneous,

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