What is the inverse of (x-3)/(x^2-4) ?

The inverse of (x-3)/(x^2-4) is (1+sqrt(1-4x(-4x+3)))/(2x),(1-sqrt(1-4x(-4x+3)))/(2x)

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inverse of (x-3)/(x^2-4)

inverse

\frac{x - 3}{x ^{2} - 4}

\frac{1 + 1 - 4 x ( - 4 x + 3 )}{2 x}, \frac{1 - 1 - 4 x ( - 4 x + 3 )}{2 x}

Solution steps

y = \frac{x - 3}{x ^{2} - 4}

Replace

x

with

y

x = \frac{y - 3}{y ^{2} - 4}

Solve for

y, x = \frac{y - 3}{y ^{2} - 4}

\frac{1 + 1 - 4 x ( - 4 x + 3 )}{2 x}, \frac{1 - 1 - 4 x ( - 4 x + 3 )}{2 x}

What is the inverse of (x-3)/(x^2-4) ?
The inverse of (x-3)/(x^2-4) is (1+sqrt(1-4x(-4x+3)))/(2x),(1-sqrt(1-4x(-4x+3)))/(2x)