Algebra Examples

$\frac{5 r^{2}}{r^{2} - 4} \cdot \frac{r + 2}{10 r^{5}}$

Step 1

Simplify the denominator.

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Step 1.1

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

$\frac{5 r^{2}}{r^{2} - 2^{2}} \cdot \frac{r + 2}{10 r^{5}}$

Step 1.2

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 $b = 2$ .

$\frac{5 r^{2}}{(r + 2) (r - 2)} \cdot \frac{r + 2}{10 r^{5}}$

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of $5 r^{2}$ .

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Step 2.1.1

Factor $5 r^{2}$ out of $10 r^{5}$ .

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

Step 2.1.2

Cancel the common factor.

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

Step 2.1.3

Rewrite the expression.

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

Step 2.2

Cancel the common factor of $r + 2$ .

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Step 2.2.1

Cancel the common factor.

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

Step 2.2.2

Rewrite the expression.

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

Step 2.3

Multiply $\frac{1}{r - 2}$ by $\frac{1}{2 r^{3}}$ .

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

Step 2.4

Simplify the expression.

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Step 2.4.1

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

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

Step 2.4.2

Reorder factors in $\frac{1}{2 (r - 2) r^{3}}$ .

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