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

The inverse of (2+x-x^2)/((x-1)^2) is (2x+1+sqrt(8x+9))/(2(x+1)),(2x+1-sqrt(8x+9))/(2(x+1))

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

inverse

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

\frac{2 x + 1 + 8 x + 9}{2 ( x + 1 )}, \frac{2 x + 1 - 8 x + 9}{2 ( x + 1 )}

Solution steps

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

Replace

x

with

y

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

Solve for

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

\frac{2 x + 1 + 8 x + 9}{2 ( x + 1 )}, \frac{2 x + 1 - 8 x + 9}{2 ( x + 1 )}

f (x) = \frac{4 x}{3 x - 2}

2^{5 - 8 x}

f (x) = - 3^{x + 1} + 9

f (x) = 6 x - 16

f (x) = 6 x - 10

What is the inverse of (2+x-x^2)/((x-1)^2) ?
The inverse of (2+x-x^2)/((x-1)^2) is (2x+1+sqrt(8x+9))/(2(x+1)),(2x+1-sqrt(8x+9))/(2(x+1))