What is the inverse of x/(x^2-25) ?

The inverse of x/(x^2-25) is (1+sqrt(1+100x^2))/(2x),(1-sqrt(1+100x^2))/(2x)

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inverse of x/(x^2-25)

inverse

\frac{x}{x ^{2} - 25}

\frac{1 + 1 + 100 x ^{2}}{2 x}, \frac{1 - 1 + 100 x ^{2}}{2 x}

Solution steps

y = \frac{x}{x ^{2} - 25}

Replace

x

with

y

x = \frac{y}{y ^{2} - 25}

Solve for

y, x = \frac{y}{y ^{2} - 25}

\frac{1 + 1 + 100 x ^{2}}{2 x}, \frac{1 - 1 + 100 x ^{2}}{2 x}

y = \frac{5 x - 7}{7 x + 6}

f (x) = \frac{1}{2} (x - 3)^{2} + 3

f (x) = \frac{1}{2} (x - 3)^{2} + 5

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

2 - 2 x + 1

What is the inverse of x/(x^2-25) ?
The inverse of x/(x^2-25) is (1+sqrt(1+100x^2))/(2x),(1-sqrt(1+100x^2))/(2x)