What is the inverse of (x-1)/(6*x*(x-1)*(x-2)) ?

The inverse of (x-1)/(6*x*(x-1)*(x-2)) is (12x+sqrt(144x^2+24x))/(12x),(12x-sqrt(144x^2+24x))/(12x)

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inverse of (x-1)/(6x(x-1)*(x-2))

inverse

\frac{x - 1}{6 \cdot x \cdot ( x - 1 ) \cdot ( x - 2 )}

\frac{12 x + 144 x ^{2} + 24 x}{12 x}, \frac{12 x - 144 x ^{2} + 24 x}{12 x}

Solution steps

y = \frac{x - 1}{6 x ( x - 1 ) ( x - 2 )}

Replace

x

with

y

x = \frac{y - 1}{6 y ( y - 1 ) ( y - 2 )}

Solve for

y, x = \frac{y - 1}{6 \cdot y \cdot ( y - 1 ) \cdot ( y - 2 )}

\frac{12 x + 144 x ^{2} + 24 x}{12 x}, \frac{12 x - 144 x ^{2} + 24 x}{12 x}

What is the inverse of (x-1)/(6*x*(x-1)*(x-2)) ?
The inverse of (x-1)/(6*x*(x-1)*(x-2)) is (12x+sqrt(144x^2+24x))/(12x),(12x-sqrt(144x^2+24x))/(12x)