What is ((x^4-2+2x^3-x))/((1-x)) ?

The solution to ((x^4-2+2x^3-x))/((1-x)) is -(x+2)(x^2+x+1)

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simplify ((x^4-2+2x^3-x))/((1-x))

simplify

\frac{( x ^{4} - 2 + 2 x ^{3} - x )}{( 1 - x )}

- (x + 2) (x^{2} + x + 1)

Solution steps

\frac{x ^{4} - 2 + 2 x ^{3} - x}{1 - x}

Factor

x^{4} - 2 + 2 x^{3} - x : (x + 2) (x - 1) (x^{2} + x + 1)

= \frac{( x + 2 ) ( x - 1 ) ( x ^{2} + x + 1 )}{1 - x}

1 - x = - (x - 1)

= \frac{( x + 2 ) ( x - 1 ) ( x ^{2} + x + 1 )}{- ( x - 1 )}

Cancel the common factor:

x - 1

= \frac{( x + 2 ) ( x ^{2} + x + 1 )}{- 1}

Apply the fraction rule:

\frac{a}{- 1} = - a

= - (x + 2) (x^{2} + x + 1)

\frac{1}{2 + 1}

\frac{3}{10} - \frac{1}{12}

4 - (- 10)

ln (e^{3}) - ln (e^{13})

(2 x - 3) (3 x^{2} - 5 x - 4)

What is ((x^4-2+2x^3-x))/((1-x)) ?
The solution to ((x^4-2+2x^3-x))/((1-x)) is -(x+2)(x^2+x+1)