Solve for y 1/y=8x

$\frac{1}{y} = 8 x$

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.

$y, 1$

The LCM of one and any expression is the expression.

$y$

Step 2

Multiply each term in $\frac{1}{y} = 8 x$ by $y$ to eliminate the fractions.

Multiply each term in $\frac{1}{y} = 8 x$ by $y$ .

$\frac{1}{y} y = 8 x y$

Simplify the left side.

Cancel the common factor of $y$ .

Cancel the common factor.

$\frac{1}{y} y = 8 x y$

Rewrite the expression.

$1 = 8 x y$

Step 3

Solve the equation.

Rewrite the equation as $8 x y = 1$ .

$8 x y = 1$

Divide each term in $8 x y = 1$ by $8 x$ and simplify.

Divide each term in $8 x y = 1$ by $8 x$ .

$\frac{8 x y}{8 x} = \frac{1}{8 x}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 x y}{8 x} = \frac{1}{8 x}$

Rewrite the expression.

$\frac{x y}{x} = \frac{1}{8 x}$

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{x y}{x} = \frac{1}{8 x}$

Divide $y$ by $1$ .

$y = \frac{1}{8 x}$