Question

Show and explain all of the steps used in order to simplify the following rational expression 3x^(2)-3x / 3x^(3)-6x^(2)+3x to 1 / x-1.

Answer 1

3x^2 + x^4 - x^3 + 3 - 6x

Explanation:

Find Least Common Multiplier of 3x^(2)-3x / 3x^(3)-6x^(2)+3x to 1 / x-1

3x^2 - 3 . x/3 x^3 - 6x^2 + 3x

Apply exponent rule: a^b + c = a^b a^c

x^2 = xx, x^3 x/3 = xx^2, x^2 = xx

= 3xx - 3xxx - 6xx + 3x

Rewrite -6 as 2 . 3

= 3xx - 3xxx + 2 . 3xx + 3x

Factor out common term 3x

= 3x(x - x^2(x/3) -2x + 1)

= 3x(- x^3/3 - x + 1)

Multiply each factor with the highest power:

(- x^3/3 - x + 1) . 3 . (1/x - 1\) . x

Simplify

3x^2 + x^4 - x^3 + 3 - 6x