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


x = -2, extraneous


x = -2, non-extraneous


x = 2, extraneous


x = 2, non-extraneous

Verified Answer :

isyllus

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.

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