How do you simplify x^3-27/3-x?

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Answer 1 · 2018-02-01T14:47:30

#= -x^2 -3x -9#

With no formatting shown, it is not clear what is given.

As it is shown, the expression means:

#x^3 -27/3 -x" "larr 3# terms separated by #+ and -# signs

Only the second term can be simplified, leading to:

#x^3 -9-x " "rarr x^3 -x-9#

However, I suspect that the question is intended to read as an algebraic fraction:

#(x^3-27)/(3-x)" "(larr"difference of cubes")/(3-x)#

Factorise the numerator: #a^3 -b^3 = (a-b)(a^2+ab+b^2)#

#=((x-3)(x^2+3x +9))/((3-x))#

Make two equal factors by dividing #-1# out of the denominator.

#[(3-x) = -(-3+x) =-(x-3)]#

#((x-3)(x^2+3x +9))/((3-x))=(cancel((x-3))(x^2+3x +9))/(-cancel((x-3)))#

#= -(x^2 +3x +9)#

#= -x^2 -3x -9#