Question

Solve 6 over x minus 3 equals 3 over x for x and determine if the solution is extraneous or not. x = −2, extraneous x = −2, non-extraneous x = −3, non-extraneous x = −3, extraneous

Answer 1

6/(x - 3) = 3/x --------------------> (x ≠ 3)

Cross multiply

6x = 3(x-3)

6x = 3x - 9

3x = -9

x = -3

answer: x = −3, non-extraneous

Answer 2

Answer:

x = −3, non-extraneous

Step-by-step explanation:

Our equation is

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

To solve this, we will cross multiply:

3(x-3) = 6(x)

Using the distributive property, we have

3(x)-3(3) = 6x

3x-9 = 6x

Subtract 3x from each side:

3x-9-3x = 6x-3x

-9 = 3x

Divide both sides by 3:

-9/3 = 3x/3

-3 = x

If we substitute -3 in for x, we do not get 0 in the denominator; this means this is a non-extraneous solution.