Question

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

Answer 1

\[\frac{4}{x+2}=\frac{2}{x}~~~~~~~~~~~THIS~?\]

Answer 2

Yes

Answer 3

\[\frac{4}{x+2}=\frac{2}{x}\]if this is true, then \[\frac{x+2}{4}=\frac{x}{2}\]must also be true

AGREE?

Answer 4

Yes

Answer 5

both sides times 4.\[x+2=2x\]\[2=2x-x\]\[2=x\]MAKES SENSE?

Answer 6

Yes it does!

Answer 7

Is it extraneous? lets plug it in.
\[\frac{4}{\color{red} {2}+2}=\frac{2}{\color{red} {2}}\]\[\frac{4}{4}=\frac{2}{2}\]So, yes, it is extraneous.

Answer 8

ok awesome really appreciate it!

Answer 9

Anytime, gavin39 !