What is the inverse of (sqrt(x+8))/(x-4) ?

The inverse of (sqrt(x+8))/(x-4) is (8x^2+1+sqrt(48x^2+1))/(2x^2),(8x^2+1-sqrt(48x^2+1))/(2x^2)

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inverse of (sqrt(x+8))/(x-4)

inverse

\frac{x + 8}{x - 4}

\frac{8 x ^{2} + 1 + 48 x ^{2} + 1}{2 x ^{2}}, \frac{8 x ^{2} + 1 - 48 x ^{2} + 1}{2 x ^{2}}

Solution steps

y = \frac{x + 8}{x - 4}

Replace

x

with

y

x = \frac{y + 8}{y - 4}

Solve for

y, x = \frac{y + 8}{y - 4}

\frac{8 x ^{2} + 1 + 48 x ^{2} + 1}{2 x ^{2}}, \frac{8 x ^{2} + 1 - 48 x ^{2} + 1}{2 x ^{2}}

What is the inverse of (sqrt(x+8))/(x-4) ?
The inverse of (sqrt(x+8))/(x-4) is (8x^2+1+sqrt(48x^2+1))/(2x^2),(8x^2+1-sqrt(48x^2+1))/(2x^2)