Pre-Algebra Examples

$\frac{4 r - 2}{r - 2} \cdot \frac{r^{2} - 4}{r - 3}$

Step 1

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

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Step 1.1

Factor $2$ out of $4 r$ .

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

Step 1.2

Factor $2$ out of $- 2$ .

$\frac{2 (2 r) + 2 (- 1)}{r - 2} \cdot \frac{r^{2} - 4}{r - 3}$

Step 1.3

Factor $2$ out of $2 (2 r) + 2 (- 1)$ .

$\frac{2 (2 r - 1)}{r - 2} \cdot \frac{r^{2} - 4}{r - 3}$

Step 2

Simplify the numerator.

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Step 2.1

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

$\frac{2 (2 r - 1)}{r - 2} \cdot \frac{r^{2} - 2^{2}}{r - 3}$

Step 2.2

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

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

Step 3

Simplify terms.

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Step 3.1

Cancel the common factor of $r - 2$ .

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Step 3.1.1

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

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

Step 3.1.2

Cancel the common factor.

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

Step 3.1.3

Rewrite the expression.

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

Step 3.2

Combine $\frac{r + 2}{r - 3}$ and $2$ .

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

Step 3.3

Move $2$ to the left of $r + 2$ .

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

Step 3.4

Multiply $\frac{2 (r + 2)}{r - 3}$ by $2 r - 1$ .

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