What is the answer to (x)^{-1}=((x+5))/((9x+1)) ?

The answer to (x)^{-1}=((x+5))/((9x+1)) is x=2+sqrt(5),x=2-sqrt(5)

Solve for x: (x)^{-1}=((x+5))/((9x+1))

The solution is x=2+sqrt(5),x=2-sqrt(5)

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(x)^{- 1} = \frac{( x + 5 )}{( 9 x + 1 )}

x = 2 + 5, x = 2 - 5

Decimal Notation

x = 4.23606 \dots, x = - 0.23606 \dots

Solution steps

x^{- 1} = \frac{( x + 5 )}{( 9 x + 1 )}

Refine

\frac{1}{x} = \frac{x + 5}{9 x + 1}

Cross multiply

9 x + 1 = x (x + 5)

Solve

9 x + 1 = x (x + 5) : x = 2 + 5, x = 2 - 5

x = 2 + 5, x = 2 - 5

Verify Solutions

Find undefined (singularity) points:

x = 0, x = - \frac{1}{9}

Combine undefined points with solutions:

x = 2 + 5, x = 2 - 5

\frac{- 4}{r + 9} = \frac{7}{- 2}

x, f = \frac{1}{x}

14 + \frac{8}{x} = 16

2 - \frac{2}{x ^{2}} = 0

(x - 1)^{- 1} = x^{- 1} + x

What is the answer to (x)^{-1}=((x+5))/((9x+1)) ?
The answer to (x)^{-1}=((x+5))/((9x+1)) is x=2+sqrt(5),x=2-sqrt(5)
Solve for x: (x)^{-1}=((x+5))/((9x+1))
The solution is x=2+sqrt(5),x=2-sqrt(5)