Basic Math Examples

$\frac{4 r - 12}{10^{2} + 20 r} \cdot \frac{5 r + 10}{24 - 8 r}$

Step 1

Factor $4$ out of $4 r - 12$ .

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Step 1.1

Factor $4$ out of $4 r$ .

$\frac{4 (r) - 12}{10^{2} + 20 r} \cdot \frac{5 r + 10}{24 - 8 r}$

Step 1.2

Factor $4$ out of $- 12$ .

$\frac{4 r + 4 \cdot - 3}{10^{2} + 20 r} \cdot \frac{5 r + 10}{24 - 8 r}$

Step 1.3

Factor $4$ out of $4 r + 4 \cdot - 3$ .

$\frac{4 (r - 3)}{10^{2} + 20 r} \cdot \frac{5 r + 10}{24 - 8 r}$

Step 2

Simplify the denominator.

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Step 2.1

Raise $10$ to the power of $2$ .

$\frac{4 (r - 3)}{100 + 20 r} \cdot \frac{5 r + 10}{24 - 8 r}$

Step 2.2

Factor $20$ out of $100 + 20 r$ .

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Step 2.2.1

Factor $20$ out of $100$ .

$\frac{4 (r - 3)}{20 \cdot 5 + 20 r} \cdot \frac{5 r + 10}{24 - 8 r}$

Step 2.2.2

Factor $20$ out of $20 \cdot 5 + 20 r$ .

$\frac{4 (r - 3)}{20 (5 + r)} \cdot \frac{5 r + 10}{24 - 8 r}$

Step 3

Simplify terms.

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Step 3.1

Factor $5$ out of $5 r + 10$ .

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Step 3.1.1

Factor $5$ out of $5 r$ .

$\frac{4 (r - 3)}{20 (5 + r)} \cdot \frac{5 (r) + 10}{24 - 8 r}$

Step 3.1.2

Factor $5$ out of $10$ .

$\frac{4 (r - 3)}{20 (5 + r)} \cdot \frac{5 r + 5 \cdot 2}{24 - 8 r}$

Step 3.1.3

Factor $5$ out of $5 r + 5 \cdot 2$ .

$\frac{4 (r - 3)}{20 (5 + r)} \cdot \frac{5 (r + 2)}{24 - 8 r}$

Step 3.2

Factor $8$ out of $24 - 8 r$ .

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Step 3.2.1

Factor $8$ out of $24$ .

$\frac{4 (r - 3)}{20 (5 + r)} \cdot \frac{5 (r + 2)}{8 (3) - 8 r}$

Step 3.2.2

Factor $8$ out of $- 8 r$ .

$\frac{4 (r - 3)}{20 (5 + r)} \cdot \frac{5 (r + 2)}{8 (3) + 8 (- r)}$

Step 3.2.3

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

$\frac{4 (r - 3)}{20 (5 + r)} \cdot \frac{5 (r + 2)}{8 (3 - r)}$

Step 3.3

Cancel the common factor of $4$ .

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Step 3.3.1

Factor $4$ out of $8 (3 - r)$ .

$\frac{4 (r - 3)}{20 (5 + r)} \cdot \frac{5 (r + 2)}{4 (2 (3 - r))}$

Step 3.3.2

Cancel the common factor.

$\frac{4 (r - 3)}{20 (5 + r)} \cdot \frac{5 (r + 2)}{4 (2 (3 - r))}$

Step 3.3.3

Rewrite the expression.

$\frac{r - 3}{20 (5 + r)} \cdot \frac{5 (r + 2)}{2 (3 - r)}$

Step 3.4

Cancel the common factor of $5$ .

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Step 3.4.1

Factor $5$ out of $20 (5 + r)$ .

$\frac{r - 3}{5 (4 (5 + r))} \cdot \frac{5 (r + 2)}{2 (3 - r)}$

Step 3.4.2

Cancel the common factor.

$\frac{r - 3}{5 (4 (5 + r))} \cdot \frac{5 (r + 2)}{2 (3 - r)}$

Step 3.4.3

Rewrite the expression.

$\frac{r - 3}{4 (5 + r)} \cdot \frac{r + 2}{2 (3 - r)}$

Step 3.5

Multiply $\frac{r - 3}{4 (5 + r)}$ by $\frac{r + 2}{2 (3 - r)}$ .

$\frac{(r - 3) (r + 2)}{4 (5 + r) (2 (3 - r))}$

Step 3.6

Multiply $2$ by $4$ .

$\frac{(r - 3) (r + 2)}{8 (5 + r) (3 - r)}$

Step 3.7

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

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Step 3.7.1

Factor $- 1$ out of $r$ .

$\frac{(- 1 (- r) - 3) (r + 2)}{8 (5 + r) (3 - r)}$

Step 3.7.2

Rewrite $- 3$ as $- 1 (3)$ .

$\frac{(- 1 (- r) - 1 (3)) (r + 2)}{8 (5 + r) (3 - r)}$

Step 3.7.3

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

$\frac{- 1 (- r + 3) (r + 2)}{8 (5 + r) (3 - r)}$

Step 3.7.4

Reorder terms.

$\frac{- 1 (- r + 3) (r + 2)}{8 (5 + r) (- r + 3)}$

Step 3.7.5

Cancel the common factor.

$\frac{- 1 (- r + 3) (r + 2)}{8 (5 + r) (- r + 3)}$

Step 3.7.6

Rewrite the expression.

$\frac{- 1 (r + 2)}{8 (5 + r)}$

Step 3.8

Move the negative in front of the fraction.

$- \frac{r + 2}{8 (5 + r)}$