Question

Solve 4 over x plus 2 equals 2 over x for x and determine if the solution is extraneous or not.

Answer 1

Answer:

The solution is x=2 and non-extraneous.

D is correct.

Step-by-step explanation:

Given: $\dfrac{4}{x+2}=\dfrac{2}{x}$

We need to solve for x.

Here we have rational expression both sides and to solve for x.

$\dfrac{4}{x+2}=\dfrac{2}{x}$

Cross multiply both sides

$4x=2(x+2)$

$4x=2x+4$

$4x-2x=4$

$2x=4$

$x=2$

Now, we will check the extraneous solution. Put x=2 into original equation.

$\dfrac{4}{2+2}=\dfrac{2}{2}$

$\dfrac{4}{4}=\dfrac{2}{2}$

$1=1$

Correct solution.

Hence, The solution is x=2 and non-extraneous.

Answer 2

X = 2, not extraneous.