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

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

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

simplify

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

x^{2} + x + 1

Solution steps

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

Factor

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

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

Cancel the common factor:

x^{2} - x - 1

= x^{2} + x + 1

\frac{y}{y ^{6}}

\frac{5 d ^{9}}{( 4 d ) ^{2}}

2 x^{4} + x^{3} - 5 x^{2} - 2 x + 2

\frac{4}{7}

\frac{1}{2} \cdot (- 8)

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