Simplify ((x-8)/(x^2-2x))÷((3x^2-24x)/(3x^2))

$\frac{x - 8}{x^{2} - 2 x} \div \frac{3 x^{2} - 24 x}{3 x^{2}}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{x - 8}{x^{2} - 2 x} \cdot \frac{3 x^{2}}{3 x^{2} - 24 x}$

Step 2

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

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

$\frac{x - 8}{x \cdot x - 2 x} \cdot \frac{3 x^{2}}{3 x^{2} - 24 x}$

Factor $x$ out of $- 2 x$ .

$\frac{x - 8}{x \cdot x + x \cdot - 2} \cdot \frac{3 x^{2}}{3 x^{2} - 24 x}$

Factor $x$ out of $x \cdot x + x \cdot - 2$ .

$\frac{x - 8}{x (x - 2)} \cdot \frac{3 x^{2}}{3 x^{2} - 24 x}$

Step 3

Cancel the common factor of $x$ .

Factor $x$ out of $3 x^{2}$ .

$\frac{x - 8}{x (x - 2)} \cdot \frac{x (3 x)}{3 x^{2} - 24 x}$

Cancel the common factor.

$\frac{x - 8}{x (x - 2)} \cdot \frac{x (3 x)}{3 x^{2} - 24 x}$

Rewrite the expression.

$\frac{x - 8}{x - 2} \cdot \frac{3 x}{3 x^{2} - 24 x}$

Step 4

Multiply $\frac{x - 8}{x - 2}$ by $\frac{3 x}{3 x^{2} - 24 x}$ .

$\frac{(x - 8) (3 x)}{(x - 2) (3 x^{2} - 24 x)}$

Step 5

Factor $3 x$ out of $3 x^{2} - 24 x$ .

Factor $3 x$ out of $3 x^{2}$ .

$\frac{(x - 8) \cdot 3 x}{(x - 2) (3 x (x) - 24 x)}$

Factor $3 x$ out of $- 24 x$ .

$\frac{(x - 8) \cdot 3 x}{(x - 2) (3 x (x) + 3 x (- 8))}$

Factor $3 x$ out of $3 x (x) + 3 x (- 8)$ .

$\frac{(x - 8) \cdot 3 x}{(x - 2) (3 x (x - 8))}$

$\frac{(x - 8) \cdot 3 x}{(x - 2) \cdot 3 x (x - 8)}$

Step 6

Cancel the common factor of $x - 8$ .

Cancel the common factor.

$\frac{(x - 8) \cdot 3 x}{(x - 2) \cdot 3 x (x - 8)}$

Rewrite the expression.

$\frac{3 x}{(x - 2) \cdot 3 x}$

Step 7

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{(x - 2) \cdot 3 x}$

Rewrite the expression.

$\frac{x}{(x - 2) x}$

Step 8

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{x}{(x - 2) x}$

Rewrite the expression.

$\frac{1}{x - 2}$

Simplify ((x-8)/(x^2-2x))÷((3x^2-24x)/(3x^2))

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