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

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

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

simplify

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

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

Solution steps

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

Multiply by the conjugate

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

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

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

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

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

3 a^{8} - 192 a^{2}

(2 u^{5} - 13 u^{4}) + (8 u^{4} + u^{5})

- 2 (a - 3 b + c)

w^{100} + w^{50}

(2 t^{2})^{3}

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