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

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

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(x+1)/(x-1)=(x-1)/(x+3)

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

x = - \frac{1}{3}

Decimal Notation

x = - 0.33333 \dots

Solution steps

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

Cross multiply

x^{2} + 4 x + 3 = x^{2} - 2 x + 1

Move

3

to the right side

x^{2} + 4 x = x^{2} - 2 x - 2

Subtract

x^{2} - 2 x

from both sides

x^{2} + 4 x - (x^{2} - 2 x) = x^{2} - 2 x - 2 - (x^{2} - 2 x)

Simplify

6 x = - 2

Divide both sides by

6

x = - \frac{1}{3}

Verify Solutions

Find undefined (singularity) points:

x = 1, x = - 3

Combine undefined points with solutions:

x = - \frac{1}{3}

6 - \frac{8}{x ^{2}} = 0

x^{- 6} - 3 x^{- 3} - 28 = 0

\frac{150 \cdot t}{t - 1} = 160

- \frac{8}{x - 4} + 1 = - \frac{x}{x - 4}

\frac{1}{10} = \frac{1}{20} + \frac{1}{x}

What is the answer to (x+1)/(x-1)=(x-1)/(x+3) ?
The answer to (x+1)/(x-1)=(x-1)/(x+3) is x=-1/3
Solve for x: (x+1)/(x-1)=(x-1)/(x+3)
The solution is x=-1/3