Section 2.4
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8x^2y : 2x : 2y = 2x
This is because 8x^2y divided over 2x leads to 4xy. Dividing 4xy over 2y leads to 2x.
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15x^6y^3 : 5y^2x^3 = 3x^3y
Note how 15 divided by 5 is 3
Also, x^6 divided by x^3 is x^3. You subtract the exponents.
Similarly, y^3 divided by y^2 is y^1 = y.
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16y^5x^3z : -4zyx = -4y^4x^2
Divide the coefficients to get 16/(-4) = -4
The y terms divide to (y^5)/(y) = y^4. Subtract the exponents.
The x and z terms are handled the same way.
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-8x^2 : 2x = -4x
We follow the same steps as before. This time -8/2 = -4 is the new coefficient. The x terms divide to (x^2)/x = x where x is nonzero.
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-6xz : -2zx = 3
The coefficients divide to (-6)/(-2) = 3
The x and z terms cancel out when we divide them.
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3y^2x : xy^2 = 3
The y^2x expression is the same as xy^2, so when we divide these terms they cancel.
. Then by the distributive property,
