Simplify 12/((10x-40)/(4/(2x-8)))

$\frac{12}{\frac{10 x - 40}{\frac{4}{2 x - 8}}}$

Step 1

Cancel the common factor of $4$ and $2 x - 8$ .

Factor $2$ out of $4$ .

$\frac{12}{\frac{10 x - 40}{\frac{2 \cdot 2}{2 x - 8}}}$

Cancel the common factors.

Factor $2$ out of $2 x$ .

$\frac{12}{\frac{10 x - 40}{\frac{2 \cdot 2}{2 (x) - 8}}}$

Factor $2$ out of $- 8$ .

$\frac{12}{\frac{10 x - 40}{\frac{2 \cdot 2}{2 (x) + 2 (- 4)}}}$

Factor $2$ out of $2 (x) + 2 (- 4)$ .

$\frac{12}{\frac{10 x - 40}{\frac{2 \cdot 2}{2 (x - 4)}}}$

Cancel the common factor.

$\frac{12}{\frac{10 x - 40}{\frac{2 \cdot 2}{2 (x - 4)}}}$

Rewrite the expression.

$\frac{12}{\frac{10 x - 40}{\frac{2}{x - 4}}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$12 \frac{\frac{2}{x - 4}}{10 x - 40}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$12 (\frac{2}{x - 4} \cdot \frac{1}{10 x - 40})$

Step 4

Factor $10$ out of $10 x - 40$ .

Factor $10$ out of $10 x$ .

$12 (\frac{2}{x - 4} \cdot \frac{1}{10 (x) - 40})$

Factor $10$ out of $- 40$ .

$12 (\frac{2}{x - 4} \cdot \frac{1}{10 x + 10 \cdot - 4})$

Factor $10$ out of $10 x + 10 \cdot - 4$ .

$12 (\frac{2}{x - 4} \cdot \frac{1}{10 (x - 4)})$

Step 5

Cancel the common factor of $2$ .

Factor $2$ out of $10 (x - 4)$ .

$12 (\frac{2}{x - 4} \cdot \frac{1}{2 (5 (x - 4))})$

Cancel the common factor.

$12 (\frac{2}{x - 4} \cdot \frac{1}{2 (5 (x - 4))})$

Rewrite the expression.

$12 (\frac{1}{x - 4} \cdot \frac{1}{5 (x - 4)})$

Step 6

Multiply $\frac{1}{x - 4}$ by $\frac{1}{5 (x - 4)}$ .

$12 \frac{1}{(x - 4) (5 (x - 4))}$

Step 7

Raise $x - 4$ to the power of $1$ .

$12 \frac{1}{5 ({(x - 4)}^{1} (x - 4))}$

Step 8

Raise $x - 4$ to the power of $1$ .

$12 \frac{1}{5 ({(x - 4)}^{1} {(x - 4)}^{1})}$

Step 9

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$12 \frac{1}{5 {(x - 4)}^{1 + 1}}$

Step 10

Add $1$ and $1$ .

$12 \frac{1}{5 {(x - 4)}^{2}}$

Step 11

Combine $12$ and $\frac{1}{5 {(x - 4)}^{2}}$ .

$\frac{12}{5 {(x - 4)}^{2}}$

Simplify 12/((10x-40)/(4/(2x-8)))

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