Algebra Examples

$\frac{a^{3} + a^{2} b}{5 a} \cdot \frac{25}{3 b + 3 a}$

Step 1

Factor $a^{2}$ out of $a^{3} + a^{2} b$ .

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Step 1.1

Factor $a^{2}$ out of $a^{3}$ .

$\frac{a^{2} a + a^{2} b}{5 a} \cdot \frac{25}{3 b + 3 a}$

Step 1.2

Factor $a^{2}$ out of $a^{2} b$ .

$\frac{a^{2} a + a^{2} (b)}{5 a} \cdot \frac{25}{3 b + 3 a}$

Step 1.3

Factor $a^{2}$ out of $a^{2} a + a^{2} (b)$ .

$\frac{a^{2} (a + b)}{5 a} \cdot \frac{25}{3 b + 3 a}$

Step 2

Factor $3$ out of $3 b + 3 a$ .

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Step 2.1

Factor $3$ out of $3 b$ .

$\frac{a^{2} (a + b)}{5 a} \cdot \frac{25}{3 (b) + 3 a}$

Step 2.2

Factor $3$ out of $3 a$ .

$\frac{a^{2} (a + b)}{5 a} \cdot \frac{25}{3 (b) + 3 (a)}$

Step 2.3

Factor $3$ out of $3 (b) + 3 (a)$ .

$\frac{a^{2} (a + b)}{5 a} \cdot \frac{25}{3 (b + a)}$

Step 3

Combine.

$\frac{a^{2} (a + b) \cdot 25}{5 a (3 (b + a))}$

Step 4

Cancel the common factor of $a^{2}$ and $a$ .

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Step 4.1

Factor $a$ out of $a^{2} (a + b) \cdot 25$ .

$\frac{a ((a (a + b)) \cdot 25)}{5 a (3 (b + a))}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $a$ out of $5 a (3 (b + a))$ .

$\frac{a ((a (a + b)) \cdot 25)}{a (5 (3 (b + a)))}$

Step 4.2.2

Cancel the common factor.

$\frac{a ((a (a + b)) \cdot 25)}{a (5 (3 (b + a)))}$

Step 4.2.3

Rewrite the expression.

$\frac{(a (a + b)) \cdot 25}{5 (3 (b + a))}$

Step 5

Cancel the common factor of $25$ and $5$ .

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Step 5.1

Factor $5$ out of $(a (a + b)) \cdot 25$ .

$\frac{5 (a (a + b) \cdot 5)}{5 (3 (b + a))}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Cancel the common factor.

$\frac{5 (a (a + b) \cdot 5)}{5 (3 (b + a))}$

Step 5.2.2

Rewrite the expression.

$\frac{a (a + b) \cdot 5}{3 (b + a)}$

Step 6

Cancel the common factor of $a + b$ and $b + a$ .

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Step 6.1

Reorder terms.

$\frac{a (a + b) \cdot 5}{3 (a + b)}$

Step 6.2

Cancel the common factor.

$\frac{a (a + b) \cdot 5}{3 (a + b)}$

Step 6.3

Rewrite the expression.

$\frac{a \cdot 5}{3}$

Step 7

Move $5$ to the left of $a$ .

$\frac{5 a}{3}$