What is the answer to 6/x = 8/((x-1)) ?

The answer to 6/x = 8/((x-1)) is x=-3

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6/x = 8/((x-1))

\frac{6}{x} = \frac{8}{( x - 1 )}

x = - 3

Solution steps

\frac{6}{x} = \frac{8}{( x - 1 )}

Cross multiply

6 x - 6 = x \cdot 8

Move

6

to the right side

6 x = x \cdot 8 + 6

Move

x 8

to the left side

- 2 x = 6

Divide both sides by

- 2

x = - 3

Verify Solutions

Find undefined (singularity) points:

x = 0, x = 1

Combine undefined points with solutions:

x = - 3

\frac{3}{x} + 3 + (- 3) = 25 + (- 3)

\frac{- 1}{2 x + 1} = - x + 8

f, f^{- 1} (x) = e^{2 x - 1}

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

\frac{5}{x} = \frac{20}{x} + 3