What is #(-12z^6u^6 + 15z^6u^3) -: (-4z^4u^5)#?

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Answer 1 · 2016-12-02T03:38:14

#3z^2u -(15z^2)/(4u^2#

The problem can also be written as:

#frac{-12z^6u^6+15z^6u^3}{-4z^4u^5}#

Then divide each of the 2 terms in the numerator by the single term in the denominator:

#frac{-12z^6u^6}{-4z^4u^5}+frac{15z^6u^3}{-4z^4u^5}#

First reduce the coeffiecients.

#-12/-4= 3# and #(15)/-4=-15/4#

#frac{3z^6u^6}{z^4u^5}-frac{15z^6u^3}{4z^4u^5}#

Now recall the exponent rule #x^a/x^b=x^(a-b)#
If #a>b# , put the variable in the numerator.
If #a< b# , put the variable in the denominator.

#3z^(6-4)u^(6-5)-frac{15z^(6-4)}{4u^(5-3)}#

#3z^2u -(15z^2)/(4u^2#