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

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

Step 1

Find the LCD of the terms in the equation.

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$x - 1, 1, 1$

Remove parentheses.

$x - 1, 1, 1$

The LCM of one and any expression is the expression.

$x - 1$

Step 2

Multiply each term in $\frac{3}{x - 1} = x + 1$ by $x - 1$ to eliminate the fractions.

Multiply each term in $\frac{3}{x - 1} = x + 1$ by $x - 1$ .

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

Simplify the left side.

Cancel the common factor of $x - 1$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the right side.

Simplify each term.

Apply the distributive property.

$3 = x \cdot x + x \cdot - 1 + 1 (x - 1)$

Multiply $x$ by $x$ .

$3 = x^{2} + x \cdot - 1 + 1 (x - 1)$

Move $- 1$ to the left of $x$ .

$3 = x^{2} - 1 \cdot x + 1 (x - 1)$

Rewrite $- 1 x$ as $- x$ .

$3 = x^{2} - x + 1 (x - 1)$

Multiply $x - 1$ by $1$ .

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

Combine the opposite terms in $x^{2} - x + x - 1$ .

Add $- x$ and $x$ .

$3 = x^{2} + 0 - 1$

Add $x^{2}$ and $0$ .

$3 = x^{2} - 1$

Step 3

Solve the equation.

Rewrite the equation as $x^{2} - 1 = 3$ .

$x^{2} - 1 = 3$

Move all terms not containing $x$ to the right side of the equation.

Add $1$ to both sides of the equation.

$x^{2} = 3 + 1$

Add $3$ and $1$ .

$x^{2} = 4$

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{4}$

Simplify $\pm \sqrt{4}$ .

Rewrite $4$ as $2^{2}$ .

$x = \pm \sqrt{2^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm 2$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x = 2$

Next, use the negative value of the $\pm$ to find the second solution.

$x = - 2$

The complete solution is the result of both the positive and negative portions of the solution.

$x = 2, - 2$

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

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