Solve for x 1+1/x=10

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

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

Subtract $1$ from both sides of the equation.

$\frac{1}{x} = 10 - 1$

Subtract $1$ from $10$ .

$\frac{1}{x} = 9$

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.

$x, 1$

The LCM of one and any expression is the expression.

$x$

Multiply each term in $\frac{1}{x} = 9$ by $x$ to eliminate the fractions.

Multiply each term in $\frac{1}{x} = 9$ by $x$ .

$\frac{1}{x} x = 9 x$

Simplify the left side.

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{1}{x} x = 9 x$

Rewrite the expression.

$1 = 9 x$

Solve the equation.

Rewrite the equation as $9 x = 1$ .

$9 x = 1$

Divide each term in $9 x = 1$ by $9$ and simplify.

Divide each term in $9 x = 1$ by $9$ .

$\frac{9 x}{9} = \frac{1}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 x}{9} = \frac{1}{9}$

Divide $x$ by $1$ .

$x = \frac{1}{9}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{9}$

Decimal Form:

$x = 0.\overline{1}$