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what are the procedures for dividing a binomial by a monomial ?

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Example given is POLYNOMIAL (3 or more terms in the numerator).  MONOMIAL is ONE term (-7x2, a3b2c), BINOMINALS are TWO terms such as a2- b2.
Here is a CORRECT EXAMPLE:   (3x2-6x )/ -21x
Look for common factors in this case 3x:
[3x (x - 2)] / [3x] (-7),  since 3x/3x = 1, cancel the terms.
You are left with (x-2) / -7


It is unconventional to leave a negative sign in the denominator, so it should instead be transferred to the numerator and distributed:
- (x - 2)
(2 - x)