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\frac{3x-9+h-3x-\left(-9\right)}{h}
To find the opposite of 3x-9, find the opposite of each term.
\frac{3x-9+h-3x+9}{h}
The opposite of -9 is 9.
\frac{-9+h+9}{h}
Combine 3x and -3x to get 0.
\frac{h}{h}
Add -9 and 9 to get 0.
1
Cancel out h in both numerator and denominator.