What is the inverse of x/(x^2-x+1) ?

The inverse of x/(x^2-x+1) is (x+1+sqrt(-3x^2+2x+1))/(2x),(x+1-sqrt(-3x^2+2x+1))/(2x)

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inverse of x/(x^2-x+1)

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

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

What is the inverse of x/(x^2-x+1) ?
The inverse of x/(x^2-x+1) is (x+1+sqrt(-3x^2+2x+1))/(2x),(x+1-sqrt(-3x^2+2x+1))/(2x)