Can I just eliminate both the (x-3) factor?

[ashen seal]

I've been taught to never eliminate factors because it can be the solution of the equation. I took this picture from the explanation of the example question, and in the explanation of the question they eliminated the (x-3) factor. Now I'm confused ...

[exotic hazel]

ok i use to eliminate this because , i think its a basic rule

[novel mauve]

U can eliminate x-3

[past quartz]

I've been taught to never eliminate factors because it can be the solution of the equation.
I think this is more the case you have say,

[atomic lantern]

Pure

[ashen seal]

Thank youu

[novel mauve]

Ah yes

We can take a case first assuming that x=3 is not a solution

And only then can we eliminate it

[exotic hazel]

Even if you dont eliminate the x-3,
That simplifies to (x-3)(x-3)=0

I dont think that changes anything

[novel mauve]

Hi chintu

[exotic hazel]

Hi

[exotic hazel]

@ashen seal You have been taught correct and today i also read a book which tells to not eliminate and keep it as factor, you can group it instead, dont be confused!

[ashen seal]

.solved

[mental hearth]

Solved

Post marked as solved by @ashen seal.

Use .unsolved if this was a mistake.

[wraith rapids]

It doesn't, because now x=3 is a solution even though the original function on the left side is not defined at x=3

[wispy pilot]

one of your x can't be equal to 3, because 3 - 3 = 0. so yes, you can eleminate x - 3, but you have to write down that x can't be equal to 3 and -3

[south delta]

.... my mind looks at that fraction and does this ....

(x - 3) / (x - 3) = 1
1 * (x + 6 ) / (x + 3) = (x + 6) / (x + 3)