Basic Math Examples

$- 2 + \frac{5 c - d}{4 c} - \frac{7 c + 5 d}{6 c}$

Step 1

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

$- 2 \cdot \frac{4 c}{4 c} + \frac{5 c - d}{4 c} - \frac{7 c + 5 d}{6 c}$

Step 2

Simplify terms.

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Step 2.1

Combine $- 2$ and $\frac{4 c}{4 c}$ .

$\frac{- 2 (4 c)}{4 c} + \frac{5 c - d}{4 c} - \frac{7 c + 5 d}{6 c}$

Step 2.2

Combine the numerators over the common denominator.

$\frac{- 2 (4 c) + 5 c - d}{4 c} - \frac{7 c + 5 d}{6 c}$

Step 3

Simplify the numerator.

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Step 3.1

Multiply $- 2$ by $4$ .

$\frac{- 8 c + 5 c - d}{4 c} - \frac{7 c + 5 d}{6 c}$

Step 3.2

Add $- 8 c$ and $5 c$ .

$\frac{- 3 c - d}{4 c} - \frac{7 c + 5 d}{6 c}$

Step 4

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

$\frac{- 3 c - d}{4 c} \cdot \frac{3}{3} - \frac{7 c + 5 d}{6 c}$

Step 5

To write $- \frac{7 c + 5 d}{6 c}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{- 3 c - d}{4 c} \cdot \frac{3}{3} - \frac{7 c + 5 d}{6 c} \cdot \frac{2}{2}$

Step 6

Write each expression with a common denominator of $12 c$ , by multiplying each by an appropriate factor of $1$ .

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Step 6.1

Multiply $\frac{- 3 c - d}{4 c}$ by $\frac{3}{3}$ .

$\frac{(- 3 c - d) \cdot 3}{4 c \cdot 3} - \frac{7 c + 5 d}{6 c} \cdot \frac{2}{2}$

Step 6.2

Multiply $3$ by $4$ .

$\frac{(- 3 c - d) \cdot 3}{12 c} - \frac{7 c + 5 d}{6 c} \cdot \frac{2}{2}$

Step 6.3

Multiply $\frac{7 c + 5 d}{6 c}$ by $\frac{2}{2}$ .

$\frac{(- 3 c - d) \cdot 3}{12 c} - \frac{(7 c + 5 d) \cdot 2}{6 c \cdot 2}$

Step 6.4

Multiply $2$ by $6$ .

$\frac{(- 3 c - d) \cdot 3}{12 c} - \frac{(7 c + 5 d) \cdot 2}{12 c}$

Step 7

Combine the numerators over the common denominator.

$\frac{(- 3 c - d) \cdot 3 - (7 c + 5 d) \cdot 2}{12 c}$

Step 8

Simplify the numerator.

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Step 8.1

Apply the distributive property.

$\frac{- 3 c \cdot 3 - d \cdot 3 - (7 c + 5 d) \cdot 2}{12 c}$

Step 8.2

Multiply $3$ by $- 3$ .

$\frac{- 9 c - d \cdot 3 - (7 c + 5 d) \cdot 2}{12 c}$

Step 8.3

Multiply $3$ by $- 1$ .

$\frac{- 9 c - 3 d - (7 c + 5 d) \cdot 2}{12 c}$

Step 8.4

Apply the distributive property.

$\frac{- 9 c - 3 d + (- (7 c) - (5 d)) \cdot 2}{12 c}$

Step 8.5

Multiply $7$ by $- 1$ .

$\frac{- 9 c - 3 d + (- 7 c - (5 d)) \cdot 2}{12 c}$

Step 8.6

Multiply $5$ by $- 1$ .

$\frac{- 9 c - 3 d + (- 7 c - 5 d) \cdot 2}{12 c}$

Step 8.7

Apply the distributive property.

$\frac{- 9 c - 3 d - 7 c \cdot 2 - 5 d \cdot 2}{12 c}$

Step 8.8

Multiply $2$ by $- 7$ .

$\frac{- 9 c - 3 d - 14 c - 5 d \cdot 2}{12 c}$

Step 8.9

Multiply $2$ by $- 5$ .

$\frac{- 9 c - 3 d - 14 c - 10 d}{12 c}$

Step 8.10

Subtract $14 c$ from $- 9 c$ .

$\frac{- 23 c - 3 d - 10 d}{12 c}$

Step 8.11

Subtract $10 d$ from $- 3 d$ .

$\frac{- 23 c - 13 d}{12 c}$

Step 9

Simplify with factoring out.

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Step 9.1

Factor $- 1$ out of $- 23 c$ .

$\frac{- (23 c) - 13 d}{12 c}$

Step 9.2

Factor $- 1$ out of $- 13 d$ .

$\frac{- (23 c) - (13 d)}{12 c}$

Step 9.3

Factor $- 1$ out of $- (23 c) - (13 d)$ .

$\frac{- (23 c + 13 d)}{12 c}$

Step 9.4

Simplify the expression.

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Step 9.4.1

Rewrite $- (23 c + 13 d)$ as $- 1 (23 c + 13 d)$ .

$\frac{- 1 (23 c + 13 d)}{12 c}$

Step 9.4.2

Move the negative in front of the fraction.

$- \frac{23 c + 13 d}{12 c}$