Algebra Examples

$\frac{7 b}{12 a} - \frac{1}{18 a b^{3}}$

Step 1

To write $\frac{7 b}{12 a}$ as a fraction with a common denominator, multiply by $\frac{3 b^{3}}{3 b^{3}}$ .

$\frac{7 b}{12 a} \cdot \frac{3 b^{3}}{3 b^{3}} - \frac{1}{18 a b^{3}}$

Step 2

To write $- \frac{1}{18 a b^{3}}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{7 b}{12 a} \cdot \frac{3 b^{3}}{3 b^{3}} - \frac{1}{18 a b^{3}} \cdot \frac{2}{2}$

Step 3

Write each expression with a common denominator of $36 a b^{3}$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{7 b}{12 a}$ by $\frac{3 b^{3}}{3 b^{3}}$ .

$\frac{7 b (3 b^{3})}{12 a (3 b^{3})} - \frac{1}{18 a b^{3}} \cdot \frac{2}{2}$

Step 3.2

Multiply $3$ by $12$ .

$\frac{7 b (3 b^{3})}{36 a b^{3}} - \frac{1}{18 a b^{3}} \cdot \frac{2}{2}$

Step 3.3

Multiply $\frac{1}{18 a b^{3}}$ by $\frac{2}{2}$ .

$\frac{7 b (3 b^{3})}{36 a b^{3}} - \frac{2}{18 a b^{3} \cdot 2}$

Step 3.4

Multiply $2$ by $18$ .

$\frac{7 b (3 b^{3})}{36 a b^{3}} - \frac{2}{36 a b^{3}}$

Step 4

Combine the numerators over the common denominator.

$\frac{7 b (3 b^{3}) - 2}{36 a b^{3}}$

Step 5

Simplify the numerator.

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Step 5.1

Rewrite using the commutative property of multiplication.

$\frac{7 \cdot 3 b \cdot b^{3} - 2}{36 a b^{3}}$

Step 5.2

Multiply $b$ by $b^{3}$ by adding the exponents.

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Step 5.2.1

Move $b^{3}$ .

$\frac{7 \cdot 3 (b^{3} b) - 2}{36 a b^{3}}$

Step 5.2.2

Multiply $b^{3}$ by $b$ .

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Step 5.2.2.1

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

$\frac{7 \cdot 3 (b^{3} b^{1}) - 2}{36 a b^{3}}$

Step 5.2.2.2

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

$\frac{7 \cdot 3 b^{3 + 1} - 2}{36 a b^{3}}$

Step 5.2.3

Add $3$ and $1$ .

$\frac{7 \cdot 3 b^{4} - 2}{36 a b^{3}}$

Step 5.3

Multiply $7$ by $3$ .

$\frac{21 b^{4} - 2}{36 a b^{3}}$