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

Question

Solve the equation

x = 2

Evaluate

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

Find the domain

More Steps

\frac{3}{x + 1} = \frac{x}{x - 1} - 1, x \in (- \infty, - 1) \cup (- 1, 1) \cup (1, + \infty)

Multiply both sides of the equation by LCD

\frac{3}{x + 1} \times (x + 1) (x - 1) = (\frac{x}{x - 1} - 1) (x + 1) (x - 1)

Simplify the equation

More Steps

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

Simplify the equation

More Steps

3 x - 3 = x + 1

Move the expression to the left side

3 x - 3 - x = 1

Move the expression to the right side

3 x - x = 1 + 3

Add and subtract

More Steps

2 x = 1 + 3

Add and subtract

2 x = 4

Divide both sides

\frac{2 x}{2} = \frac{4}{2}

Divide the numbers

x = \frac{4}{2}

Divide the numbers

More Steps

x = 2

Check if the solution is in the defined range

x = 2, x \in (- \infty, - 1) \cup (- 1, 1) \cup (1, + \infty)

Solution

x = 2

Show Solution