Algebra Examples

$\frac{a}{12 b} - \frac{b}{8 a}$

Step 1

To write $\frac{a}{12 b}$ as a fraction with a common denominator, multiply by $\frac{2 a}{2 a}$ .

$\frac{a}{12 b} \cdot \frac{2 a}{2 a} - \frac{b}{8 a}$

Step 2

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

$\frac{a}{12 b} \cdot \frac{2 a}{2 a} - \frac{b}{8 a} \cdot \frac{3 b}{3 b}$

Step 3

Write each expression with a common denominator of $24 b a$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{a}{12 b}$ by $\frac{2 a}{2 a}$ .

$\frac{a (2 a)}{12 b (2 a)} - \frac{b}{8 a} \cdot \frac{3 b}{3 b}$

Step 3.2

Multiply $2$ by $12$ .

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

Step 3.3

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

$\frac{a (2 a)}{24 b a} - \frac{b (3 b)}{8 a (3 b)}$

Step 3.4

Multiply $3$ by $8$ .

$\frac{a (2 a)}{24 b a} - \frac{b (3 b)}{24 a b}$

Step 3.5

Reorder the factors of $24 b a$ .

$\frac{a (2 a)}{24 a b} - \frac{b (3 b)}{24 a b}$

Step 4

Combine the numerators over the common denominator.

$\frac{a (2 a) - b (3 b)}{24 a b}$

Step 5

Simplify the numerator.

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Step 5.1

Rewrite using the commutative property of multiplication.

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

Step 5.2

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

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Step 5.2.1

Move $a$ .

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

Step 5.2.2

Multiply $a$ by $a$ .

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

Step 5.3

Rewrite using the commutative property of multiplication.

$\frac{2 a^{2} - 1 \cdot 3 b \cdot b}{24 a b}$

Step 5.4

Multiply $b$ by $b$ by adding the exponents.

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Step 5.4.1

Move $b$ .

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

Step 5.4.2

Multiply $b$ by $b$ .

$\frac{2 a^{2} - 1 \cdot 3 b^{2}}{24 a b}$

Step 5.5

Multiply $- 1$ by $3$ .

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