Solve for x (6-x)/x=10

$\frac{6 - x}{x} = 10$

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.

$x, 1$

The LCM of one and any expression is the expression.

$x$

Step 2

Multiply each term in $\frac{6 - x}{x} = 10$ by $x$ to eliminate the fractions.

Multiply each term in $\frac{6 - x}{x} = 10$ by $x$ .

$\frac{6 - x}{x} x = 10 x$

Simplify the left side.

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{6 - x}{x} x = 10 x$

Rewrite the expression.

$6 - x = 10 x$

Step 3

Solve the equation.

Move all terms containing $x$ to the left side of the equation.

Subtract $10 x$ from both sides of the equation.

$6 - x - 10 x = 0$

Subtract $10 x$ from $- x$ .

$6 - 11 x = 0$

Subtract $6$ from both sides of the equation.

$- 11 x = - 6$

Divide each term in $- 11 x = - 6$ by $- 11$ and simplify.

Divide each term in $- 11 x = - 6$ by $- 11$ .

$\frac{- 11 x}{- 11} = \frac{- 6}{- 11}$

Simplify the left side.

Cancel the common factor of $- 11$ .

Cancel the common factor.

$\frac{- 11 x}{- 11} = \frac{- 6}{- 11}$

Divide $x$ by $1$ .

$x = \frac{- 6}{- 11}$

Simplify the right side.

Dividing two negative values results in a positive value.

$x = \frac{6}{11}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{6}{11}$

Decimal Form:

$x = 0.\overline{54}$