Question

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

Answer 1

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

Answer 2

mhmm

Answer 3

this is why mathematicians invented notation instead of using words

Answer 4

if you like you can start by flipping both sides and solve \[\frac{x+2}{4}=\frac{x}{2}\]

Answer 5

or just go right to \[4x=2(x+2)\]

Answer 6

are w solving for 'x'

Answer 7

we*

Answer 8

\[\frac{a}{b}=\frac{c}{d}\iff ad=bc\] is always true
yes you are solving for \(x\) there is not other variable there

Answer 9

x=2

Answer 10

yes that is correct
if \(x=2\) then both sides of the equal sign are \(1\)

Answer 11

correct, i don't know what the following step is though

Answer 12

to determine if this is extraneous or not

Answer 13

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 14

thank you @satellite73