Basic Math Examples

$\frac{7 r - 21 s}{6 r - 12 s} \div \frac{9 s - 3 r}{2 r - 4 s}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{7 r - 21 s}{6 r - 12 s} \cdot \frac{2 r - 4 s}{9 s - 3 r}$

Step 2

Simplify terms.

Tap for more steps...

Step 2.1

Factor $7$ out of $7 r - 21 s$ .

Tap for more steps...

Step 2.1.1

Factor $7$ out of $7 r$ .

$\frac{7 (r) - 21 s}{6 r - 12 s} \cdot \frac{2 r - 4 s}{9 s - 3 r}$

Step 2.1.2

Factor $7$ out of $- 21 s$ .

$\frac{7 (r) + 7 (- 3 s)}{6 r - 12 s} \cdot \frac{2 r - 4 s}{9 s - 3 r}$

Step 2.1.3

Factor $7$ out of $7 (r) + 7 (- 3 s)$ .

$\frac{7 (r - 3 s)}{6 r - 12 s} \cdot \frac{2 r - 4 s}{9 s - 3 r}$

Step 2.2

Factor $6$ out of $6 r - 12 s$ .

Tap for more steps...

Step 2.2.1

Factor $6$ out of $6 r$ .

$\frac{7 (r - 3 s)}{6 (r) - 12 s} \cdot \frac{2 r - 4 s}{9 s - 3 r}$

Step 2.2.2

Factor $6$ out of $- 12 s$ .

$\frac{7 (r - 3 s)}{6 (r) + 6 (- 2 s)} \cdot \frac{2 r - 4 s}{9 s - 3 r}$

Step 2.2.3

Factor $6$ out of $6 (r) + 6 (- 2 s)$ .

$\frac{7 (r - 3 s)}{6 (r - 2 s)} \cdot \frac{2 r - 4 s}{9 s - 3 r}$

Step 2.3

Factor $2$ out of $2 r - 4 s$ .

Tap for more steps...

Step 2.3.1

Factor $2$ out of $2 r$ .

$\frac{7 (r - 3 s)}{6 (r - 2 s)} \cdot \frac{2 (r) - 4 s}{9 s - 3 r}$

Step 2.3.2

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

$\frac{7 (r - 3 s)}{6 (r - 2 s)} \cdot \frac{2 (r) + 2 (- 2 s)}{9 s - 3 r}$

Step 2.3.3

Factor $2$ out of $2 (r) + 2 (- 2 s)$ .

$\frac{7 (r - 3 s)}{6 (r - 2 s)} \cdot \frac{2 (r - 2 s)}{9 s - 3 r}$

Step 2.4

Factor $3$ out of $9 s - 3 r$ .

Tap for more steps...

Step 2.4.1

Factor $3$ out of $9 s$ .

$\frac{7 (r - 3 s)}{6 (r - 2 s)} \cdot \frac{2 (r - 2 s)}{3 (3 s) - 3 r}$

Step 2.4.2

Factor $3$ out of $- 3 r$ .

$\frac{7 (r - 3 s)}{6 (r - 2 s)} \cdot \frac{2 (r - 2 s)}{3 (3 s) + 3 (- r)}$

Step 2.4.3

Factor $3$ out of $3 (3 s) + 3 (- r)$ .

$\frac{7 (r - 3 s)}{6 (r - 2 s)} \cdot \frac{2 (r - 2 s)}{3 (3 s - r)}$

Step 2.5

Cancel the common factor of $2 (r - 2 s)$ .

Tap for more steps...

Step 2.5.1

Factor $2 (r - 2 s)$ out of $6 (r - 2 s)$ .

$\frac{7 (r - 3 s)}{2 (r - 2 s) (3)} \cdot \frac{2 (r - 2 s)}{3 (3 s - r)}$

Step 2.5.2

Cancel the common factor.

$\frac{7 (r - 3 s)}{2 (r - 2 s) \cdot 3} \cdot \frac{2 (r - 2 s)}{3 (3 s - r)}$

Step 2.5.3

Rewrite the expression.

$\frac{7 (r - 3 s)}{3} \cdot \frac{1}{3 (3 s - r)}$

Step 2.6

Multiply $\frac{7 (r - 3 s)}{3}$ by $\frac{1}{3 (3 s - r)}$ .

$\frac{7 (r - 3 s)}{3 (3 (3 s - r))}$

Step 2.7

Multiply $3$ by $3$ .

$\frac{7 (r - 3 s)}{9 (3 s - r)}$

Step 2.8

Cancel the common factor of $r - 3 s$ and $3 s - r$ .

Tap for more steps...

Step 2.8.1

Factor $- 1$ out of $r$ .

$\frac{7 (- 1 (- r) - 3 s)}{9 (3 s - r)}$

Step 2.8.2

Factor $- 1$ out of $- 3 s$ .

$\frac{7 (- 1 (- r) - (3 s))}{9 (3 s - r)}$

Step 2.8.3

Factor $- 1$ out of $- 1 (- r) - (3 s)$ .

$\frac{7 (- 1 (- r + 3 s))}{9 (3 s - r)}$

Step 2.8.4

Reorder terms.

$\frac{7 (- 1 (- r + 3 s))}{9 (- r + 3 s)}$

Step 2.8.5

Cancel the common factor.

$\frac{7 (- 1 (- r + 3 s))}{9 (- r + 3 s)}$

Step 2.8.6

Rewrite the expression.

$\frac{7 \cdot (- 1)}{9}$

Step 3

Multiply $7$ by $- 1$ .

$\frac{- 7}{9}$

Step 4

Move the negative in front of the fraction.

$- \frac{7}{9}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{7}{9}$

Decimal Form:

$- 0.\overline{7}$