Solve for x 1/x=y

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

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 $\frac{1}{x} = y$ by $x$ to eliminate the fractions.

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

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

Simplify the left side.

Cancel the common factor of $x$ .

Cancel the common factor.

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

Rewrite the expression.

$1 = y x$

Solve the equation.

Rewrite the equation as $y x = 1$ .

$y x = 1$

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

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

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

Simplify the left side.

Cancel the common factor of $y$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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