Algebra Examples

$\frac{b^{2}}{6 a^{2}} - \frac{1}{3 a^{3}} + \frac{3 b}{8 a}$

Step 1

To write $\frac{b^{2}}{6 a^{2}}$ as a fraction with a common denominator, multiply by $\frac{a}{a}$ .

$\frac{b^{2}}{6 a^{2}} \cdot \frac{a}{a} - \frac{1}{3 a^{3}} + \frac{3 b}{8 a}$

Step 2

To write $- \frac{1}{3 a^{3}}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{b^{2}}{6 a^{2}} \cdot \frac{a}{a} - \frac{1}{3 a^{3}} \cdot \frac{2}{2} + \frac{3 b}{8 a}$

Step 3

Write each expression with a common denominator of $6 a^{3}$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{b^{2}}{6 a^{2}}$ by $\frac{a}{a}$ .

$\frac{b^{2} a}{6 a^{2} a} - \frac{1}{3 a^{3}} \cdot \frac{2}{2} + \frac{3 b}{8 a}$

Step 3.2

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

$\frac{b^{2} a}{6 (a^{1} a^{2})} - \frac{1}{3 a^{3}} \cdot \frac{2}{2} + \frac{3 b}{8 a}$

Step 3.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{b^{2} a}{6 a^{1 + 2}} - \frac{1}{3 a^{3}} \cdot \frac{2}{2} + \frac{3 b}{8 a}$

Step 3.4

Add $1$ and $2$ .

$\frac{b^{2} a}{6 a^{3}} - \frac{1}{3 a^{3}} \cdot \frac{2}{2} + \frac{3 b}{8 a}$

Step 3.5

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

$\frac{b^{2} a}{6 a^{3}} - \frac{2}{3 a^{3} \cdot 2} + \frac{3 b}{8 a}$

Step 3.6

Multiply $2$ by $3$ .

$\frac{b^{2} a}{6 a^{3}} - \frac{2}{6 a^{3}} + \frac{3 b}{8 a}$

Step 4

Combine the numerators over the common denominator.

$\frac{b^{2} a - 2}{6 a^{3}} + \frac{3 b}{8 a}$

Step 5

To write $\frac{b^{2} a - 2}{6 a^{3}}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{b^{2} a - 2}{6 a^{3}} \cdot \frac{4}{4} + \frac{3 b}{8 a}$

Step 6

To write $\frac{3 b}{8 a}$ as a fraction with a common denominator, multiply by $\frac{3 a^{2}}{3 a^{2}}$ .

$\frac{b^{2} a - 2}{6 a^{3}} \cdot \frac{4}{4} + \frac{3 b}{8 a} \cdot \frac{3 a^{2}}{3 a^{2}}$

Step 7

Write each expression with a common denominator of $24 a^{3}$ , by multiplying each by an appropriate factor of $1$ .

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Step 7.1

Multiply $\frac{b^{2} a - 2}{6 a^{3}}$ by $\frac{4}{4}$ .

$\frac{(b^{2} a - 2) \cdot 4}{6 a^{3} \cdot 4} + \frac{3 b}{8 a} \cdot \frac{3 a^{2}}{3 a^{2}}$

Step 7.2

Multiply $4$ by $6$ .

$\frac{(b^{2} a - 2) \cdot 4}{24 a^{3}} + \frac{3 b}{8 a} \cdot \frac{3 a^{2}}{3 a^{2}}$

Step 7.3

Multiply $\frac{3 b}{8 a}$ by $\frac{3 a^{2}}{3 a^{2}}$ .

$\frac{(b^{2} a - 2) \cdot 4}{24 a^{3}} + \frac{3 b (3 a^{2})}{8 a (3 a^{2})}$

Step 7.4

Multiply $3$ by $8$ .

$\frac{(b^{2} a - 2) \cdot 4}{24 a^{3}} + \frac{3 b (3 a^{2})}{24 a \cdot a^{2}}$

Step 7.5

Multiply $a$ by $a^{2}$ by adding the exponents.

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Step 7.5.1

Move $a^{2}$ .

$\frac{(b^{2} a - 2) \cdot 4}{24 a^{3}} + \frac{3 b (3 a^{2})}{24 (a^{2} a)}$

Step 7.5.2

Multiply $a^{2}$ by $a$ .

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Step 7.5.2.1

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

$\frac{(b^{2} a - 2) \cdot 4}{24 a^{3}} + \frac{3 b (3 a^{2})}{24 (a^{2} a^{1})}$

Step 7.5.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{(b^{2} a - 2) \cdot 4}{24 a^{3}} + \frac{3 b (3 a^{2})}{24 a^{2 + 1}}$

Step 7.5.3

Add $2$ and $1$ .

$\frac{(b^{2} a - 2) \cdot 4}{24 a^{3}} + \frac{3 b (3 a^{2})}{24 a^{3}}$

Step 8

Combine the numerators over the common denominator.

$\frac{(b^{2} a - 2) \cdot 4 + 3 b (3 a^{2})}{24 a^{3}}$

Step 9

Simplify the numerator.

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Step 9.1

Apply the distributive property.

$\frac{b^{2} a \cdot 4 - 2 \cdot 4 + 3 b \cdot 3 a^{2}}{24 a^{3}}$

Step 9.2

Move $4$ to the left of $b^{2} a$ .

$\frac{4 \cdot (b^{2} a) - 2 \cdot 4 + 3 b \cdot 3 a^{2}}{24 a^{3}}$

Step 9.3

Multiply $- 2$ by $4$ .

$\frac{4 \cdot (b^{2} a) - 8 + 3 b \cdot 3 a^{2}}{24 a^{3}}$

Step 9.4

Remove parentheses.

$\frac{4 b^{2} a - 8 + 3 b \cdot 3 a^{2}}{24 a^{3}}$

Step 9.5

Multiply $3$ by $3$ .

$\frac{4 b^{2} a - 8 + 9 b a^{2}}{24 a^{3}}$