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

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

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

inverse

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

\frac{2 x ^{2} + 1 + 12 x ^{2} + 1}{2 x ^{2}}, \frac{2 x ^{2} + 1 - 12 x ^{2} + 1}{2 x ^{2}}

Solution steps

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

Replace

x

with

y

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

Solve for

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

\frac{2 x ^{2} + 1 + 12 x ^{2} + 1}{2 x ^{2}}, \frac{2 x ^{2} + 1 - 12 x ^{2} + 1}{2 x ^{2}}

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