Simplify (a^3+a^2b)/(5a)*25/(3b+3a)

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

Step 1

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

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

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

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

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

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 $3 b + 3 a$ .

Factor $3$ out of $3 b$ .

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

Factor $3$ out of $3 a$ .

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

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 $a$ .

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

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 5

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

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

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

Cancel the common factors.

Cancel the common factor.

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

Rewrite the expression.

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

Step 6

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

Reorder terms.

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 7

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

$\frac{5 a}{3}$

Simplify (a^3+a^2b)/(5a)*25/(3b+3a)

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