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

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

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.

$x + 1, 1$

Remove parentheses.

$x + 1, 1$

The LCM of one and any expression is the expression.

$x + 1$

Step 2

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

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

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

Simplify the left side.

Cancel the common factor of $x + 1$ .

Cancel the common factor.

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

Rewrite the expression.

$1 = 3 (x + 1)$

Simplify the right side.

Apply the distributive property.

$1 = 3 x + 3 \cdot 1$

Multiply $3$ by $1$ .

$1 = 3 x + 3$

Step 3

Solve the equation.

Rewrite the equation as $3 x + 3 = 1$ .

$3 x + 3 = 1$

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

Subtract $3$ from both sides of the equation.

$3 x = 1 - 3$

Subtract $3$ from $1$ .

$3 x = - 2$

Divide each term in $3 x = - 2$ by $3$ and simplify.

Divide each term in $3 x = - 2$ by $3$ .

$\frac{3 x}{3} = \frac{- 2}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 2}{3}$

Divide $x$ by $1$ .

$x = \frac{- 2}{3}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{2}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{2}{3}$

Decimal Form:

$x = - 0.\overline{6}$

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

Related Questions

Support LCMGCF.com by disabling your adblocker.