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

The inverse of 2+1/(x^2-3x) is (3x-6+sqrt(9x^2-32x+28))/(2(x-2)),(3x-6-sqrt(9x^2-32x+28))/(2(x-2))

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inverse of 2+1/(x^2-3x)

inverse

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

\frac{3 x - 6 + 9 x ^{2} - 32 x + 28}{2 ( x - 2 )}, \frac{3 x - 6 - 9 x ^{2} - 32 x + 28}{2 ( x - 2 )}

Solution steps

y = 2 + \frac{1}{x ^{2} - 3 x}

Replace

x

with

y

x = 2 + \frac{1}{y ^{2} - 3 y}

Solve for

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

\frac{3 x - 6 + 9 x ^{2} - 32 x + 28}{2 ( x - 2 )}, \frac{3 x - 6 - 9 x ^{2} - 32 x + 28}{2 ( x - 2 )}

12 x

f (x) = 9 x^{2} + 1

f (x) = 9 x^{2} + 8

f (x) = 3 8 - x + 7

f (x) = 9 x^{2} + 7

What is the inverse of 2+1/(x^2-3x) ?
The inverse of 2+1/(x^2-3x) is (3x-6+sqrt(9x^2-32x+28))/(2(x-2)),(3x-6-sqrt(9x^2-32x+28))/(2(x-2))