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

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

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

simplify

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

x^{2} + 1

Solution steps

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

Factor

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

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

Apply the commutative law:

1 + x = x + 1

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

Cancel the common factor:

x + 1

= x^{2} + 1

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

x^{2} + 6 2 x + 10

d (d - 1) - 4 (d^{'}) - 4 d^{'} - 1

1 7^{\frac{1}{2}} \cdot 1 7^{\frac{1}{2}}

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

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