Algebra Examples

$\frac{3 b}{4 a^{2}} + \frac{1}{8 a} - \frac{5 b^{2}}{6 a^{3}}$

Step 1

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

$\frac{3 b}{4 a^{2}} \cdot \frac{2}{2} + \frac{1}{8 a} - \frac{5 b^{2}}{6 a^{3}}$

Step 2

To write $\frac{1}{8 a}$ as a fraction with a common denominator, multiply by $\frac{a}{a}$ .

$\frac{3 b}{4 a^{2}} \cdot \frac{2}{2} + \frac{1}{8 a} \cdot \frac{a}{a} - \frac{5 b^{2}}{6 a^{3}}$

Step 3

Write each expression with a common denominator of $8 a^{2}$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

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

$\frac{3 b \cdot 2}{4 a^{2} \cdot 2} + \frac{1}{8 a} \cdot \frac{a}{a} - \frac{5 b^{2}}{6 a^{3}}$

Step 3.2

Multiply $2$ by $4$ .

$\frac{3 b \cdot 2}{8 a^{2}} + \frac{1}{8 a} \cdot \frac{a}{a} - \frac{5 b^{2}}{6 a^{3}}$

Step 3.3

Multiply $\frac{1}{8 a}$ by $\frac{a}{a}$ .

$\frac{3 b \cdot 2}{8 a^{2}} + \frac{a}{8 a \cdot a} - \frac{5 b^{2}}{6 a^{3}}$

Step 3.4

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

$\frac{3 b \cdot 2}{8 a^{2}} + \frac{a}{8 (a^{1} a)} - \frac{5 b^{2}}{6 a^{3}}$

Step 3.5

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

$\frac{3 b \cdot 2}{8 a^{2}} + \frac{a}{8 (a^{1} a^{1})} - \frac{5 b^{2}}{6 a^{3}}$

Step 3.6

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

$\frac{3 b \cdot 2}{8 a^{2}} + \frac{a}{8 a^{1 + 1}} - \frac{5 b^{2}}{6 a^{3}}$

Step 3.7

Add $1$ and $1$ .

$\frac{3 b \cdot 2}{8 a^{2}} + \frac{a}{8 a^{2}} - \frac{5 b^{2}}{6 a^{3}}$

Step 4

Combine the numerators over the common denominator.

$\frac{3 b \cdot 2 + a}{8 a^{2}} - \frac{5 b^{2}}{6 a^{3}}$

Step 5

Multiply $2$ by $3$ .

$\frac{6 b + a}{8 a^{2}} - \frac{5 b^{2}}{6 a^{3}}$

Step 6

To write $\frac{6 b + a}{8 a^{2}}$ as a fraction with a common denominator, multiply by $\frac{3 a}{3 a}$ .

$\frac{6 b + a}{8 a^{2}} \cdot \frac{3 a}{3 a} - \frac{5 b^{2}}{6 a^{3}}$

Step 7

To write $- \frac{5 b^{2}}{6 a^{3}}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{6 b + a}{8 a^{2}} \cdot \frac{3 a}{3 a} - \frac{5 b^{2}}{6 a^{3}} \cdot \frac{4}{4}$

Step 8

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 8.1

Multiply $\frac{6 b + a}{8 a^{2}}$ by $\frac{3 a}{3 a}$ .

$\frac{(6 b + a) (3 a)}{8 a^{2} (3 a)} - \frac{5 b^{2}}{6 a^{3}} \cdot \frac{4}{4}$

Step 8.2

Multiply $3$ by $8$ .

$\frac{(6 b + a) (3 a)}{24 a^{2} a} - \frac{5 b^{2}}{6 a^{3}} \cdot \frac{4}{4}$

Step 8.3

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

$\frac{(6 b + a) (3 a)}{24 (a^{1} a^{2})} - \frac{5 b^{2}}{6 a^{3}} \cdot \frac{4}{4}$

Step 8.4

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

$\frac{(6 b + a) (3 a)}{24 a^{1 + 2}} - \frac{5 b^{2}}{6 a^{3}} \cdot \frac{4}{4}$

Step 8.5

Add $1$ and $2$ .

$\frac{(6 b + a) (3 a)}{24 a^{3}} - \frac{5 b^{2}}{6 a^{3}} \cdot \frac{4}{4}$

Step 8.6

Multiply $\frac{5 b^{2}}{6 a^{3}}$ by $\frac{4}{4}$ .

$\frac{(6 b + a) (3 a)}{24 a^{3}} - \frac{5 b^{2} \cdot 4}{6 a^{3} \cdot 4}$

Step 8.7

Multiply $4$ by $6$ .

$\frac{(6 b + a) (3 a)}{24 a^{3}} - \frac{5 b^{2} \cdot 4}{24 a^{3}}$

Step 9

Combine the numerators over the common denominator.

$\frac{(6 b + a) (3 a) - 5 b^{2} \cdot 4}{24 a^{3}}$

Step 10

Simplify the numerator.

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Step 10.1

Apply the distributive property.

$\frac{(6 b \cdot 3 + a \cdot 3) a - 5 b^{2} \cdot 4}{24 a^{3}}$

Step 10.2

Multiply $3$ by $6$ .

$\frac{(18 b + a \cdot 3) a - 5 b^{2} \cdot 4}{24 a^{3}}$

Step 10.3

Move $3$ to the left of $a$ .

$\frac{(18 b + 3 \cdot a) a - 5 b^{2} \cdot 4}{24 a^{3}}$

Step 10.4

Apply the distributive property.

$\frac{18 b a + 3 a \cdot a - 5 b^{2} \cdot 4}{24 a^{3}}$

Step 10.5

Multiply $a$ by $a$ by adding the exponents.

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Step 10.5.1

Move $a$ .

$\frac{18 b a + 3 (a \cdot a) - 5 b^{2} \cdot 4}{24 a^{3}}$

Step 10.5.2

Multiply $a$ by $a$ .

$\frac{18 b a + 3 a^{2} - 5 b^{2} \cdot 4}{24 a^{3}}$

Step 10.6

Multiply $4$ by $- 5$ .

$\frac{18 b a + 3 a^{2} - 20 b^{2}}{24 a^{3}}$