Question

Solve 6/×-3 =x/3

for x, and determine if the solution is extraneous or not.
x = -2. extraneous
x = -2, non-extraneous
X = -3. non-extraneous
x = -3. extraneous​

Answer 1

X = -3. non-extraneous

Explanation:

The given equation is
`(6)/(x-3) =(x)/(3)`

We cross multiply to get:

`6*3=x(x-3)`

Expand and multiply.

`18=x^2-3x`

`x^2-3x-18=0`

We factor to obtain:

`(x-6)(x+3)=0`

`x=-3,x=6`

Checking for extraneous solutions

Substitute x=-3
`(6)/(-3-3) =(-3)/(3)`

`(6)/(-6) =(-3)/(3)`

`-1=-1`

`1=1`.....Non-extraneous

Checking for x=6

`(6)/(6-3) =(6)/(3)`

`(6)/(3) =(6)/(3)`

`2=2`....Non-extraneous