Question

Solve for 4/x+2 = 2/x  x and determine if the solution is extraneous or not.

x = −2, extraneous
x = −2, non-extraneous
x = 2, extraneous
x = 2, non-extraneous

Answer 1

The given equation is:

4/(x + 2) = 2/x

First we get the value of x by doing cross multiplication so that all variables are in the numerator side:

4 x = 2 (x + 2)

4 x = 2 x + 4

2 x = 4

x = 2

An extraneous solution is one in which if we plug in the value of x back into the equation, the resulting values would be wrong.

Plug x = 2 back into the original equation:

4 / (2 + 2) = 2 / 2

4 / 4 = 2 / 2

1 = 1 (TRUE!)

Since the value of x = 2 satisfies the equation, then the solution is non-extraneous.

Answer:

x = 2, non-extraneous