Solve for x x/(x^2-6x)=1

$\frac{x}{x^{2} - 6 x} = 1$

Step 1

Factor each term.

Factor $x$ out of $x^{2} - 6 x$ .

Factor $x$ out of $x^{2}$ .

$\frac{x}{x \cdot x - 6 x} = 1$

Factor $x$ out of $- 6 x$ .

$\frac{x}{x \cdot x + x \cdot - 6} = 1$

Factor $x$ out of $x \cdot x + x \cdot - 6$ .

$\frac{x}{x (x - 6)} = 1$

Reduce the expression $\frac{x}{x (x - 6)}$ by cancelling the common factors.

Cancel the common factor.

$\frac{x}{x (x - 6)} = 1$

Rewrite the expression.

$\frac{1}{x - 6} = 1$

Step 2

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.

$x - 6, 1$

Remove parentheses.

$x - 6, 1$

The LCM of one and any expression is the expression.

$x - 6$

Step 3

Multiply each term in $\frac{1}{x - 6} = 1$ by $x - 6$ to eliminate the fractions.

Multiply each term in $\frac{1}{x - 6} = 1$ by $x - 6$ .

$\frac{1}{x - 6} (x - 6) = 1 (x - 6)$

Simplify the left side.

Cancel the common factor of $x - 6$ .

Cancel the common factor.

$\frac{1}{x - 6} (x - 6) = 1 (x - 6)$

Rewrite the expression.

$1 = 1 (x - 6)$

Simplify the right side.

Multiply $x - 6$ by $1$ .

$1 = x - 6$

Step 4

Solve the equation.

Rewrite the equation as $x - 6 = 1$ .

$x - 6 = 1$

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

Add $6$ to both sides of the equation.

$x = 1 + 6$

Add $1$ and $6$ .

$x = 7$