Algebra Examples

$\frac{4 a}{5 b^{3}} + \frac{6 a}{2}$

Step 1

Cancel the common factor of $6$ and $2$ .

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Step 1.1

Factor $2$ out of $6 a$ .

$\frac{4 a}{5 b^{3}} + \frac{2 (3 a)}{2}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $2$ out of $2$ .

$\frac{4 a}{5 b^{3}} + \frac{2 (3 a)}{2 (1)}$

Step 1.2.2

Cancel the common factor.

$\frac{4 a}{5 b^{3}} + \frac{2 (3 a)}{2 \cdot 1}$

Step 1.2.3

Rewrite the expression.

$\frac{4 a}{5 b^{3}} + \frac{3 a}{1}$

Step 1.2.4

Divide $3 a$ by $1$ .

$\frac{4 a}{5 b^{3}} + 3 a$

Step 2

To write $3 a$ as a fraction with a common denominator, multiply by $\frac{5 b^{3}}{5 b^{3}}$ .

$\frac{4 a}{5 b^{3}} + 3 a \cdot \frac{5 b^{3}}{5 b^{3}}$

Step 3

Simplify terms.

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Step 3.1

Combine $3 a$ and $\frac{5 b^{3}}{5 b^{3}}$ .

$\frac{4 a}{5 b^{3}} + \frac{3 a (5 b^{3})}{5 b^{3}}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{4 a + 3 a (5 b^{3})}{5 b^{3}}$

Step 4

Simplify the numerator.

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Step 4.1

Factor $a$ out of $4 a + 3 a \cdot 5 b^{3}$ .

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Step 4.1.1

Factor $a$ out of $4 a$ .

$\frac{a \cdot 4 + 3 a \cdot 5 b^{3}}{5 b^{3}}$

Step 4.1.2

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

$\frac{a \cdot 4 + a (3 \cdot 5 b^{3})}{5 b^{3}}$

Step 4.1.3

Factor $a$ out of $a \cdot 4 + a (3 \cdot 5 b^{3})$ .

$\frac{a (4 + 3 \cdot 5 b^{3})}{5 b^{3}}$

Step 4.2

Multiply $3$ by $5$ .

$\frac{a (4 + 15 b^{3})}{5 b^{3}}$