Why can't x-2/x-6 simplify to 1/3?

Answer 1

Because (x-2).(x-6) = 1/3 ONLY if x = 0

Answer 2

x-2/x-6

x - (2/x) - 6

wherever did you get 1/3 ?

Answer 3

1/3 =

1/3 * (x - 2)/(x - 2) =

1(x - 2)/(3(x - 2)) =

(x - 2)/(3x - 6), not (x - 2)/(x - 6)

Answer 4

Is x - (2/x) - 6 the same as 1/3? It depends on the value of x.

x - (2/x) - 6 = 1/3

Multiply through by 3x:

3x^2 - 6 - 18x = x

3x^2 - 18x - 6 - x = 0

3x^2 - 19x - 6 = 0

x = (-(-19) +/- sqrt((-19)^2 - 4(3)(-6))) / (2*3)

x = (19 +/- sqrt(361 + 72)) / 6

x = (19 +/- sqrt(433)) / 6

x =~ 6.6347753411141352717951502536839 or -0.30144200778080193846181692035056

So if x is one of those two values, then yes, you can simplify like that, but otherwise, no.

Or did you mean:

(x - 2) / (x - 6) = 1/3

Cross-multiply:

3(x - 2) = x - 6

3x - 6 = x - 6

3x - 6 - x + 6 = 0

2x = 0

x = 0/2

x = 0

So if x = 0, then yes, you can simplify like that, but otherwise, no.

Answer 5

x - 2 and x - 6 are not  common factors and cannot be equal to 1/3..

Answer 6

Let x = 4 

Hence 

(4 - 2)/(4 - 6) = 

2/2 = 1 

This is just an example of using a non-zero number to show that (x -2)/(x -6) is no simply '1/3'. 

Answer 7

Assuming this is (x - 2) / (x - 6), x - 2 is one expression by itself and shares no common and cancellable factors with x - 6.  However, if x = 0, the entire rational expression will equal 1/3 ((0 - 2) / (0 - 6) = -2 / -6 = 1/3).

Answer 8

Assuming you meant (x-2)/(x-6)

let's try one example to disprove it's 1/3:

If x = 2, then

(2-2)/(2-6) = 0, so you know for sure it's not 1/3

In fact, it's 1/3 for only where x=0, all other values it's some other value.

Answer 9

(x - 2) / (x - 6)

Because x isn't a factor so you can't just divide both sides by it to cancel them out.

That's like saying:

8 / 4

and you want to cancel out a 10 (x = 10 from your example).

That doesn't work.

Answer 10

(x - 2)/(x - 6)

= x/(x - 6) - 2/(x - 6)

Root:

x = 2