Basic Math Examples

$\frac{4 b - 9}{2 b} + \frac{5 b - 1}{6 b}$

Step 1

To write $\frac{4 b - 9}{2 b}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{4 b - 9}{2 b} \cdot \frac{3}{3} + \frac{5 b - 1}{6 b}$

Step 2

Write each expression with a common denominator of $6 b$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.1

Multiply $\frac{4 b - 9}{2 b}$ by $\frac{3}{3}$ .

$\frac{(4 b - 9) \cdot 3}{2 b \cdot 3} + \frac{5 b - 1}{6 b}$

Step 2.2

Multiply $3$ by $2$ .

$\frac{(4 b - 9) \cdot 3}{6 b} + \frac{5 b - 1}{6 b}$

Step 3

Combine the numerators over the common denominator.

$\frac{(4 b - 9) \cdot 3 + 5 b - 1}{6 b}$

Step 4

Simplify the numerator.

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Step 4.1

Apply the distributive property.

$\frac{4 b \cdot 3 - 9 \cdot 3 + 5 b - 1}{6 b}$

Step 4.2

Multiply $3$ by $4$ .

$\frac{12 b - 9 \cdot 3 + 5 b - 1}{6 b}$

Step 4.3

Multiply $- 9$ by $3$ .

$\frac{12 b - 27 + 5 b - 1}{6 b}$

Step 4.4

Add $12 b$ and $5 b$ .

$\frac{17 b - 27 - 1}{6 b}$

Step 4.5

Subtract $1$ from $- 27$ .

$\frac{17 b - 28}{6 b}$