Precalculus Examples

$1 - \frac{3 c + 2 d}{6 c} + \frac{3 c - 7 d}{9 c}$

Step 1

Combine into one fraction.

Tap for more steps...

Step 1.1

Write $1$ as a fraction with a common denominator.

$\frac{6 c}{6 c} - \frac{3 c + 2 d}{6 c} + \frac{3 c - 7 d}{9 c}$

Step 1.2

Combine the numerators over the common denominator.

$\frac{6 c - (3 c + 2 d)}{6 c} + \frac{3 c - 7 d}{9 c}$

Step 2

Simplify the numerator.

Tap for more steps...

Step 2.1

Apply the distributive property.

$\frac{6 c - (3 c) - (2 d)}{6 c} + \frac{3 c - 7 d}{9 c}$

Step 2.2

Multiply $3$ by $- 1$ .

$\frac{6 c - 3 c - (2 d)}{6 c} + \frac{3 c - 7 d}{9 c}$

Step 2.3

Multiply $2$ by $- 1$ .

$\frac{6 c - 3 c - 2 d}{6 c} + \frac{3 c - 7 d}{9 c}$

Step 2.4

Subtract $3 c$ from $6 c$ .

$\frac{3 c - 2 d}{6 c} + \frac{3 c - 7 d}{9 c}$

Step 3

To write $\frac{3 c - 2 d}{6 c}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{3 c - 2 d}{6 c} \cdot \frac{3}{3} + \frac{3 c - 7 d}{9 c}$

Step 4

To write $\frac{3 c - 7 d}{9 c}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{3 c - 2 d}{6 c} \cdot \frac{3}{3} + \frac{3 c - 7 d}{9 c} \cdot \frac{2}{2}$

Step 5

Write each expression with a common denominator of $18 c$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 5.1

Multiply $\frac{3 c - 2 d}{6 c}$ by $\frac{3}{3}$ .

$\frac{(3 c - 2 d) \cdot 3}{6 c \cdot 3} + \frac{3 c - 7 d}{9 c} \cdot \frac{2}{2}$

Step 5.2

Multiply $3$ by $6$ .

$\frac{(3 c - 2 d) \cdot 3}{18 c} + \frac{3 c - 7 d}{9 c} \cdot \frac{2}{2}$

Step 5.3

Multiply $\frac{3 c - 7 d}{9 c}$ by $\frac{2}{2}$ .

$\frac{(3 c - 2 d) \cdot 3}{18 c} + \frac{(3 c - 7 d) \cdot 2}{9 c \cdot 2}$

Step 5.4

Multiply $2$ by $9$ .

$\frac{(3 c - 2 d) \cdot 3}{18 c} + \frac{(3 c - 7 d) \cdot 2}{18 c}$

Step 6

Combine the numerators over the common denominator.

$\frac{(3 c - 2 d) \cdot 3 + (3 c - 7 d) \cdot 2}{18 c}$

Step 7

Simplify the numerator.

Tap for more steps...

Step 7.1

Apply the distributive property.

$\frac{3 c \cdot 3 - 2 d \cdot 3 + (3 c - 7 d) \cdot 2}{18 c}$

Step 7.2

Multiply $3$ by $3$ .

$\frac{9 c - 2 d \cdot 3 + (3 c - 7 d) \cdot 2}{18 c}$

Step 7.3

Multiply $3$ by $- 2$ .

$\frac{9 c - 6 d + (3 c - 7 d) \cdot 2}{18 c}$

Step 7.4

Apply the distributive property.

$\frac{9 c - 6 d + 3 c \cdot 2 - 7 d \cdot 2}{18 c}$

Step 7.5

Multiply $2$ by $3$ .

$\frac{9 c - 6 d + 6 c - 7 d \cdot 2}{18 c}$

Step 7.6

Multiply $2$ by $- 7$ .

$\frac{9 c - 6 d + 6 c - 14 d}{18 c}$

Step 7.7

Add $9 c$ and $6 c$ .

$\frac{15 c - 6 d - 14 d}{18 c}$

Step 7.8

Subtract $14 d$ from $- 6 d$ .

$\frac{15 c - 20 d}{18 c}$

Step 7.9

Factor $5$ out of $15 c - 20 d$ .

Tap for more steps...

Step 7.9.1

Factor $5$ out of $15 c$ .

$\frac{5 (3 c) - 20 d}{18 c}$

Step 7.9.2

Factor $5$ out of $- 20 d$ .

$\frac{5 (3 c) + 5 (- 4 d)}{18 c}$

Step 7.9.3

Factor $5$ out of $5 (3 c) + 5 (- 4 d)$ .

$\frac{5 (3 c - 4 d)}{18 c}$