Pre-Algebra Examples

$\frac{\frac{x^{2} - 4}{21 x}}{\frac{2 - 4}{7 x y}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{x^{2} - 4}{21 x} \cdot \frac{7 x y}{2 - 4}$

Step 2

Cancel the common factor of $7 x$ .

Tap for more steps...

Step 2.1

Factor $7 x$ out of $21 x$ .

$\frac{x^{2} - 4}{7 x (3)} \cdot \frac{7 x y}{2 - 4}$

Step 2.2

Factor $7 x$ out of $7 x y$ .

$\frac{x^{2} - 4}{7 x (3)} \cdot \frac{7 x (y)}{2 - 4}$

Step 2.3

Cancel the common factor.

$\frac{x^{2} - 4}{7 x \cdot 3} \cdot \frac{7 x y}{2 - 4}$

Step 2.4

Rewrite the expression.

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

Step 3

Multiply $\frac{x^{2} - 4}{3}$ by $\frac{y}{2 - 4}$ .

$\frac{(x^{2} - 4) y}{3 (2 - 4)}$

Step 4

Simplify the numerator.

Tap for more steps...

Step 4.1

Rewrite $4$ as $2^{2}$ .

$\frac{(x^{2} - 2^{2}) y}{3 (2 - 4)}$

Step 4.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 2$ .

$\frac{(x + 2) (x - 2) y}{3 (2 - 4)}$

Step 5

Subtract $4$ from $2$ .

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

Step 6

Multiply $3$ by $- 2$ .

$\frac{(x + 2) (x - 2) y}{- 6}$

Step 7

Move the negative in front of the fraction.

$- \frac{(x + 2) (x - 2) y}{6}$

Step 8

Reorder factors in $- \frac{(x + 2) (x - 2) y}{6}$ .

$- \frac{y (x + 2) (x - 2)}{6}$

Step 9

Apply the distributive property.

$- \frac{(y x + y \cdot 2) (x - 2)}{6}$

Step 10

Move $2$ to the left of $y$ .

$- \frac{(y x + 2 \cdot y) (x - 2)}{6}$

Step 11

Expand $(y x + 2 y) (x - 2)$ using the FOIL Method.

Tap for more steps...

Step 11.1

Apply the distributive property.

$- \frac{y x (x - 2) + 2 y (x - 2)}{6}$

Step 11.2

Apply the distributive property.

$- \frac{y x \cdot x + y x \cdot - 2 + 2 y (x - 2)}{6}$

Step 11.3

Apply the distributive property.

$- \frac{y x \cdot x + y x \cdot - 2 + 2 y x + 2 y \cdot - 2}{6}$

Step 12

Combine the opposite terms in $y x \cdot x + y x \cdot - 2 + 2 y x + 2 y \cdot - 2$ .

Tap for more steps...

Step 12.1

Reorder the factors in the terms $y x \cdot - 2$ and $2 y x$ .

$- \frac{y x \cdot x - 2 x y + 2 x y + 2 y \cdot - 2}{6}$

Step 12.2

Add $- 2 x y$ and $2 x y$ .

$- \frac{y x \cdot x + 0 + 2 y \cdot - 2}{6}$

Step 12.3

Add $y x \cdot x$ and $0$ .

$- \frac{y x \cdot x + 2 y \cdot - 2}{6}$

Step 13

Simplify each term.

Tap for more steps...

Step 13.1

Multiply $x$ by $x$ by adding the exponents.

Tap for more steps...

Step 13.1.1

Move $x$ .

$- \frac{y (x \cdot x) + 2 y \cdot - 2}{6}$

Step 13.1.2

Multiply $x$ by $x$ .

$- \frac{y x^{2} + 2 y \cdot - 2}{6}$

Step 13.2

Multiply $- 2$ by $2$ .

$- \frac{y x^{2} - 4 y}{6}$

Step 14

Split the fraction $\frac{y x^{2} - 4 y}{6}$ into two fractions.

$- (\frac{y x^{2}}{6} + \frac{- 4 y}{6})$

Step 15

Cancel the common factor of $- 4$ and $6$ .

Tap for more steps...

Step 15.1

Factor $2$ out of $- 4 y$ .

$- (\frac{y x^{2}}{6} + \frac{2 (- 2 y)}{6})$

Step 15.2

Cancel the common factors.

Tap for more steps...

Step 15.2.1

Factor $2$ out of $6$ .

$- (\frac{y x^{2}}{6} + \frac{2 (- 2 y)}{2 (3)})$

Step 15.2.2

Cancel the common factor.

$- (\frac{y x^{2}}{6} + \frac{2 (- 2 y)}{2 \cdot 3})$

Step 15.2.3

Rewrite the expression.

$- (\frac{y x^{2}}{6} + \frac{- 2 y}{3})$

Step 16

Move the negative in front of the fraction.

$- (\frac{y x^{2}}{6} - \frac{2 y}{3})$