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When can, or can't, terms be cancelled.
ie: $\frac{3x^2-1}{x^2}$
$x^2$ cannot be cancelled. Why not, and what are the rules?
2 Answers
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Since “canceling” means “dividing the numerator and the denominator by the same (non-zero) number” one might cancel the given fraction by $7$, e.g., which yields to $\dfrac{\dfrac{3x^2}{7}-\dfrac{1}{7}}{\dfrac{x^2}{7}},$ which is perfectly right and perfectly senseless either.
Moral: canceling means not simplifying per se. If simplifying is the goal, first factorize numerator and denominator and look for common factors.
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- Anything trig over/above something not trig.
1.a. unlike trig functions.
- Anytime there exists a higher power of a variable above or below some smaller power.
- Anytime there is a constant above or below with addition or subtraction operators with variables.
And of course this is all given that a series of variables with powers doesn't equal the below or above.
