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How Do You Divide Quotients of Monomials?

Divide these rational expressions:

Summary

  1. Change the division to multiplication using the reciprocal rule of division
  2. Cancel out any common factors that you can
  3. Rewrite the factors that are left before you multiply
  4. Finally, multiply the monomials to find our answer

Notes

    1. You can always change any kind of division into multiplication by using the reciprocal rule
    1. This is the principle of the reciprocal rule of division
    1. You can only do this because of the reciprocal rule of division
    1. We need to find and then cancel out common factors in the numerator and denominator
    1. 2 is a factor in the monomial 2x2y
    1. x2 is a factor in the monomial 2x2y
    1. y is a factor in the monomial 2x2y
    2. y is also a factor of the monomial 3yz in the denominator
    3. Since y is a factor in both the numerator and denominator, we can cancel it
    1. 16 is a factor in 16xd2
    1. We already know that there are no x's in the denominator for an x to cancel with
    2. The x in 16xd2 just stays there.
    3. There is only one monomial with a d in it, so we can't cancel it out with anything else
    1. It'll be easier to multiply everything together if we know what terms are left to multiply
    1. Remember, we canceled out the y's in the original fraction
    1. Now we can multiply the monomials together in the numerators and denominators
    1. Multiply the monomials together in the numerators and denominators
    2. The numerators: 2x2•16xd2=32x3d2
    3. The denominators: 3z•9y2z=27y2z2
    1. Use the reciprocal rule of division to change division to multiplication
    2. Find factors that are in both the numerator and denominator and cancel them
    3. Rewriting the problem will help us multiply things later
    4. Multiply the numerators and denominators straight across to simplify