Pre-Algebra Examples

$\frac{\frac{4 - x}{x^{2} - 16 x}}{\frac{12 - 3 x}{x - 4}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{4 - x}{x^{2} - 16 x} \cdot \frac{x - 4}{12 - 3 x}$

Step 2

Factor $x$ out of $x^{2} - 16 x$ .

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Step 2.1

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

$\frac{4 - x}{x \cdot x - 16 x} \cdot \frac{x - 4}{12 - 3 x}$

Step 2.2

Factor $x$ out of $- 16 x$ .

$\frac{4 - x}{x \cdot x + x \cdot - 16} \cdot \frac{x - 4}{12 - 3 x}$

Step 2.3

Factor $x$ out of $x \cdot x + x \cdot - 16$ .

$\frac{4 - x}{x (x - 16)} \cdot \frac{x - 4}{12 - 3 x}$

Step 3

Factor $3$ out of $12 - 3 x$ .

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Step 3.1

Factor $3$ out of $12$ .

$\frac{4 - x}{x (x - 16)} \cdot \frac{x - 4}{3 (4) - 3 x}$

Step 3.2

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

$\frac{4 - x}{x (x - 16)} \cdot \frac{x - 4}{3 (4) + 3 (- x)}$

Step 3.3

Factor $3$ out of $3 (4) + 3 (- x)$ .

$\frac{4 - x}{x (x - 16)} \cdot \frac{x - 4}{3 (4 - x)}$

Step 4

Cancel the common factor of $4 - x$ .

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Step 4.1

Factor $4 - x$ out of $3 (4 - x)$ .

$\frac{4 - x}{x (x - 16)} \cdot \frac{x - 4}{(4 - x) \cdot 3}$

Step 4.2

Cancel the common factor.

$\frac{4 - x}{x (x - 16)} \cdot \frac{x - 4}{(4 - x) \cdot 3}$

Step 4.3

Rewrite the expression.

$\frac{1}{x (x - 16)} \cdot \frac{x - 4}{3}$

Step 5

Multiply $\frac{1}{x (x - 16)}$ by $\frac{x - 4}{3}$ .

$\frac{x - 4}{x (x - 16) \cdot 3}$

Step 6

Move $3$ to the left of $x (x - 16)$ .

$\frac{x - 4}{3 x (x - 16)}$

Step 7

Split the fraction $\frac{x - 4}{3 x (x - 16)}$ into two fractions.

$\frac{x}{3 x (x - 16)} + \frac{- 4}{3 x (x - 16)}$

Step 8

Cancel the common factor of $x$ .

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Step 8.1

Cancel the common factor.

$\frac{x}{3 x (x - 16)} + \frac{- 4}{3 x (x - 16)}$

Step 8.2

Rewrite the expression.

$\frac{1}{3 (x - 16)} + \frac{- 4}{3 x (x - 16)}$

Step 9

Move the negative in front of the fraction.

$\frac{1}{3 (x - 16)} - \frac{4}{3 x (x - 16)}$