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What is the quotient of #-18x^-2+27x^-2-72x^-8# and 9x?

Answer 1

Eli Assouline

#x^-3 - 8x^-9# or #1/x^3 - 8/x^9#

This problem can be written as, what is:

#(-18x^-2 + 27x^-2 - 72x^-8)/(9x)#

First, we can combine like terms:

#((-18 + 27)x^-2 - 72x^-8)/(9x)#

#(9x^-2 - 72x^-8)/(9x)#

We can now rewrite this as two separate fractions:

#(9x^-2)/(9x) - (72x^-8)/(9x)#

#(9/9)(x^-2/x^1) - (72/9)(x^-8/x^1)#

Dividing the constants and using the rules of exponents we get:

#1(x^(-2-1))# - 8(x^(-8 - 1))#

#x^-3 - 8x^-9#

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Answer 2

Jace Anderson

The quotient of -18x^-2+27x^-2-72x^-8 and 9x is -2x^-3 + 3x^-3 - 8x^-9.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.