Simplify (20b^2)/(30a^2)+(10ab^3)/(5ab)

$\frac{20 b^{2}}{30 a^{2}} + \frac{10 a b^{3}}{5 a b}$

Simplify each term.

Cancel the common factor of $20$ and $30$ .

Factor $10$ out of $20 b^{2}$ .

$\frac{10 (2 b^{2})}{30 a^{2}} + \frac{10 a b^{3}}{5 a b}$

Cancel the common factors.

Factor $10$ out of $30 a^{2}$ .

$\frac{10 (2 b^{2})}{10 (3 a^{2})} + \frac{10 a b^{3}}{5 a b}$

Cancel the common factor.

$\frac{10 (2 b^{2})}{10 (3 a^{2})} + \frac{10 a b^{3}}{5 a b}$

Rewrite the expression.

$\frac{2 b^{2}}{3 a^{2}} + \frac{10 a b^{3}}{5 a b}$

Cancel the common factor of $10$ and $5$ .

Factor $5$ out of $10 a b^{3}$ .

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

Cancel the common factors.

Factor $5$ out of $5 a b$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{2 b^{2}}{3 a^{2}} + \frac{2 a b^{3}}{a b}$

Cancel the common factor of $a$ .

Cancel the common factor.

$\frac{2 b^{2}}{3 a^{2}} + \frac{2 a b^{3}}{a b}$

Rewrite the expression.

$\frac{2 b^{2}}{3 a^{2}} + \frac{2 b^{3}}{b}$

Cancel the common factor of $b^{3}$ and $b$ .

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

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

Cancel the common factors.

Raise $b$ to the power of $1$ .

$\frac{2 b^{2}}{3 a^{2}} + \frac{b (2 b^{2})}{b^{1}}$

Factor $b$ out of $b^{1}$ .

$\frac{2 b^{2}}{3 a^{2}} + \frac{b (2 b^{2})}{b \cdot 1}$

Cancel the common factor.

$\frac{2 b^{2}}{3 a^{2}} + \frac{b (2 b^{2})}{b \cdot 1}$

Rewrite the expression.

$\frac{2 b^{2}}{3 a^{2}} + \frac{2 b^{2}}{1}$

Divide $2 b^{2}$ by $1$ .

$\frac{2 b^{2}}{3 a^{2}} + 2 b^{2}$

To write $2 b^{2}$ as a fraction with a common denominator, multiply by $\frac{3 a^{2}}{3 a^{2}}$ .

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

Combine $2 b^{2}$ and $\frac{3 a^{2}}{3 a^{2}}$ .

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

Combine the numerators over the common denominator.

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

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

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

$\frac{2 b^{2} (1) + 2 b^{2} \cdot 3 a^{2}}{3 a^{2}}$

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

$\frac{2 b^{2} (1) + 2 b^{2} (3 a^{2})}{3 a^{2}}$

Factor $2 b^{2}$ out of $2 b^{2} (1) + 2 b^{2} (3 a^{2})$ .

$\frac{2 b^{2} (1 + 3 a^{2})}{3 a^{2}}$

Simplify (20b^2)/(30a^2)+(10ab^3)/(5ab)

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