What is the answer to (x-1)/(x^2-1)=3 ?

The answer to (x-1)/(x^2-1)=3 is x=-2/3

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(x-1)/(x^2-1)=3

\frac{x - 1}{x ^{2} - 1} = 3

x = - \frac{2}{3}

Solution steps

\frac{x - 1}{x ^{2} - 1} = 3

Simplify

\frac{x - 1}{x ^{2} - 1} : \frac{1}{x + 1}

\frac{1}{x + 1} = 3

Multiply both sides by

x + 1

1 = 3 (x + 1)

Switch sides

3 (x + 1) = 1

Divide both sides by

3

x + 1 = \frac{1}{3}

Move

1

to the right side

x = - \frac{2}{3}

Verify Solutions

Find undefined (singularity) points:

x = 1, x = - 1

Combine undefined points with solutions:

x = - \frac{2}{3}

y, \frac{x}{y} + 9 = n

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

\frac{x + 1}{2 x - 3} = \frac{5}{6}

2 F - G = \frac{D}{h}

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