My best mistake of the week was simplifying a rational expression incorrectly by not factoring first. I canceled out too soon and thought i was done, but I left out important steps that need to be done in order to simplify it.
-Question with Error
The error I made was in the question:
I attempted to cancel out the x right away:
That was wrong because I split the numerator and denominator into separate terms instead of factoring the whole expressions.
The way to do it is to factor the numerator and denominator:
Numerator is:
x^2 − 9 = (x−3)(x+3)
Denominator:
x^2 – x – 6 = (x -3)(x + 2)
With this the expression becomes:
Now I need to cancel the common factor:
-What I Learned
I learned that you can cancel only entire factors, not terms. Factor first and then simplify. Its also important consider limitations on the variable (like x ≠ 3)
so you won’t divide by zero. Now I do not forget to factor carefully, take my time, and look for common factors instead of going ahead and canceling out things that aren‘t exactly common.