Question

Classify the solutions of 1 over x plus 4, plus one half, equals 1 over x plus 4 as extraneous or non-extraneous.

Answer 1

X=-4 ; extraneous is your answer

Answer 2

x=-4 , Extraneous

Explanation:

Given : Equation -
`(1)/(x+4)+ (1)/(2)=(1)/(x+4)`

To classify : The given equation as extraneous or non-extraneous ?

Solution :

An extraneous solution is one that we arrive at that will not work in the equation.

For rational equations, extraneous solutions are ones that will cause the denominator to be 0.

So, first we solve the given equation

`(1)/(x+4)+ (1)/(2)=(1)/(x+4)`

Taking LCM to LHS

`(2+x+4)/(2(x+4))=(1)/(x+4)`

Cancel (x+4) both side,

`(x+6)/(2)=1`

Cross multiply,

`x+6=2`

`x=-4`

Now, if we put x=-4 in the equation the denominator is zero.

Therefore, It is an extraneous solution.