Basic Math Examples

$\frac{8}{7 a b} - \frac{3}{14 a^{2} b} + \frac{5}{21 a b^{2}}$

Step 1

To write $\frac{8}{7 a b}$ as a fraction with a common denominator, multiply by $\frac{2 a}{2 a}$ .

$\frac{8}{7 a b} \cdot \frac{2 a}{2 a} - \frac{3}{14 a^{2} b} + \frac{5}{21 a b^{2}}$

Step 2

Write each expression with a common denominator of $14 b a^{2}$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.1

Multiply $\frac{8}{7 a b}$ by $\frac{2 a}{2 a}$ .

$\frac{8 (2 a)}{7 a b (2 a)} - \frac{3}{14 a^{2} b} + \frac{5}{21 a b^{2}}$

Step 2.2

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

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Step 2.2.1

Move $a$ .

$\frac{8 (2 a)}{7 (a \cdot a) b \cdot 2} - \frac{3}{14 a^{2} b} + \frac{5}{21 a b^{2}}$

Step 2.2.2

Multiply $a$ by $a$ .

$\frac{8 (2 a)}{7 a^{2} b \cdot 2} - \frac{3}{14 a^{2} b} + \frac{5}{21 a b^{2}}$

Step 2.3

Multiply $2$ by $7$ .

$\frac{8 (2 a)}{14 a^{2} b} - \frac{3}{14 a^{2} b} + \frac{5}{21 a b^{2}}$

Step 3

Combine the numerators over the common denominator.

$\frac{8 (2 a) - 3}{14 a^{2} b} + \frac{5}{21 a b^{2}}$

Step 4

Multiply $8$ by $2$ .

$\frac{16 a - 3}{14 a^{2} b} + \frac{5}{21 a b^{2}}$

Step 5

To write $\frac{16 a - 3}{14 a^{2} b}$ as a fraction with a common denominator, multiply by $\frac{3 b}{3 b}$ .

$\frac{16 a - 3}{14 a^{2} b} \cdot \frac{3 b}{3 b} + \frac{5}{21 a b^{2}}$

Step 6

To write $\frac{5}{21 a b^{2}}$ as a fraction with a common denominator, multiply by $\frac{2 a}{2 a}$ .

$\frac{16 a - 3}{14 a^{2} b} \cdot \frac{3 b}{3 b} + \frac{5}{21 a b^{2}} \cdot \frac{2 a}{2 a}$

Step 7

Write each expression with a common denominator of $42 a^{2} b^{2}$ , by multiplying each by an appropriate factor of $1$ .

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Step 7.1

Multiply $\frac{16 a - 3}{14 a^{2} b}$ by $\frac{3 b}{3 b}$ .

$\frac{(16 a - 3) (3 b)}{14 a^{2} b (3 b)} + \frac{5}{21 a b^{2}} \cdot \frac{2 a}{2 a}$

Step 7.2

Multiply $3$ by $14$ .

$\frac{(16 a - 3) (3 b)}{42 a^{2} b \cdot b} + \frac{5}{21 a b^{2}} \cdot \frac{2 a}{2 a}$

Step 7.3

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

$\frac{(16 a - 3) (3 b)}{42 a^{2} (b^{1} b)} + \frac{5}{21 a b^{2}} \cdot \frac{2 a}{2 a}$

Step 7.4

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

$\frac{(16 a - 3) (3 b)}{42 a^{2} (b^{1} b^{1})} + \frac{5}{21 a b^{2}} \cdot \frac{2 a}{2 a}$

Step 7.5

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

$\frac{(16 a - 3) (3 b)}{42 a^{2} b^{1 + 1}} + \frac{5}{21 a b^{2}} \cdot \frac{2 a}{2 a}$

Step 7.6

Add $1$ and $1$ .

$\frac{(16 a - 3) (3 b)}{42 a^{2} b^{2}} + \frac{5}{21 a b^{2}} \cdot \frac{2 a}{2 a}$

Step 7.7

Multiply $\frac{5}{21 a b^{2}}$ by $\frac{2 a}{2 a}$ .

$\frac{(16 a - 3) (3 b)}{42 a^{2} b^{2}} + \frac{5 (2 a)}{21 a b^{2} (2 a)}$

Step 7.8

Multiply $2$ by $21$ .

$\frac{(16 a - 3) (3 b)}{42 a^{2} b^{2}} + \frac{5 (2 a)}{42 a b^{2} a}$

Step 7.9

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

$\frac{(16 a - 3) (3 b)}{42 a^{2} b^{2}} + \frac{5 (2 a)}{42 (a^{1} a) b^{2}}$

Step 7.10

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

$\frac{(16 a - 3) (3 b)}{42 a^{2} b^{2}} + \frac{5 (2 a)}{42 (a^{1} a^{1}) b^{2}}$

Step 7.11

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

$\frac{(16 a - 3) (3 b)}{42 a^{2} b^{2}} + \frac{5 (2 a)}{42 a^{1 + 1} b^{2}}$

Step 7.12

Add $1$ and $1$ .

$\frac{(16 a - 3) (3 b)}{42 a^{2} b^{2}} + \frac{5 (2 a)}{42 a^{2} b^{2}}$

Step 8

Combine the numerators over the common denominator.

$\frac{(16 a - 3) (3 b) + 5 (2 a)}{42 a^{2} b^{2}}$

Step 9

Simplify the numerator.

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Step 9.1

Apply the distributive property.

$\frac{(16 a \cdot 3 - 3 \cdot 3) b + 5 \cdot 2 a}{42 a^{2} b^{2}}$

Step 9.2

Multiply $3$ by $16$ .

$\frac{(48 a - 3 \cdot 3) b + 5 \cdot 2 a}{42 a^{2} b^{2}}$

Step 9.3

Multiply $- 3$ by $3$ .

$\frac{(48 a - 9) b + 5 \cdot 2 a}{42 a^{2} b^{2}}$

Step 9.4

Apply the distributive property.

$\frac{48 a b - 9 b + 5 \cdot 2 a}{42 a^{2} b^{2}}$

Step 9.5

Multiply $5$ by $2$ .

$\frac{48 a b - 9 b + 10 a}{42 a^{2} b^{2}}$