Answer:
The solution is x=2 and non-extraneous.
D is correct.
Step-by-step explanation:
Given: [tex]\dfrac{4}{x+2}=\dfrac{2}{x}[/tex]
We need to solve for x.
Here we have rational expression both sides and to solve for x.
[tex]\dfrac{4}{x+2}=\dfrac{2}{x}[/tex]
Cross multiply both sides
[tex]4x=2(x+2)[/tex]
[tex]4x=2x+4[/tex]
[tex]4x-2x=4[/tex]
[tex]2x=4[/tex]
[tex]x=2[/tex]
Now, we will check the extraneous solution. Put x=2 into original equation.
[tex]\dfrac{4}{2+2}=\dfrac{2}{2}[/tex]
[tex]\dfrac{4}{4}=\dfrac{2}{2}[/tex]
[tex]1=1[/tex]
Correct solution.
Hence, The solution is x=2 and non-extraneous.
