Basic Math Examples

$- 3 + \frac{7 c - 7 d}{2 c} - \frac{5 c - 8 d}{6 c}$

Step 1

Factor $7$ out of $7 c - 7 d$ .

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Step 1.1

Factor $7$ out of $7 c$ .

$- 3 + \frac{7 (c) - 7 d}{2 c} - \frac{5 c - 8 d}{6 c}$

Step 1.2

Factor $7$ out of $- 7 d$ .

$- 3 + \frac{7 (c) + 7 (- d)}{2 c} - \frac{5 c - 8 d}{6 c}$

Step 1.3

Factor $7$ out of $7 (c) + 7 (- d)$ .

$- 3 + \frac{7 (c - d)}{2 c} - \frac{5 c - 8 d}{6 c}$

Step 2

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

$- 3 \cdot \frac{2 c}{2 c} + \frac{7 (c - d)}{2 c} - \frac{5 c - 8 d}{6 c}$

Step 3

Simplify terms.

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Step 3.1

Combine $- 3$ and $\frac{2 c}{2 c}$ .

$\frac{- 3 (2 c)}{2 c} + \frac{7 (c - d)}{2 c} - \frac{5 c - 8 d}{6 c}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{- 3 (2 c) + 7 (c - d)}{2 c} - \frac{5 c - 8 d}{6 c}$

Step 4

Simplify the numerator.

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Step 4.1

Multiply $- 3$ by $2$ .

$\frac{- 6 c + 7 (c - d)}{2 c} - \frac{5 c - 8 d}{6 c}$

Step 4.2

Apply the distributive property.

$\frac{- 6 c + 7 c + 7 (- d)}{2 c} - \frac{5 c - 8 d}{6 c}$

Step 4.3

Multiply $- 1$ by $7$ .

$\frac{- 6 c + 7 c - 7 d}{2 c} - \frac{5 c - 8 d}{6 c}$

Step 4.4

Add $- 6 c$ and $7 c$ .

$\frac{c - 7 d}{2 c} - \frac{5 c - 8 d}{6 c}$

Step 5

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

$\frac{c - 7 d}{2 c} \cdot \frac{3}{3} - \frac{5 c - 8 d}{6 c}$

Step 6

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

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Step 6.1

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

$\frac{(c - 7 d) \cdot 3}{2 c \cdot 3} - \frac{5 c - 8 d}{6 c}$

Step 6.2

Multiply $3$ by $2$ .

$\frac{(c - 7 d) \cdot 3}{6 c} - \frac{5 c - 8 d}{6 c}$

Step 7

Combine the numerators over the common denominator.

$\frac{(c - 7 d) \cdot 3 - (5 c - 8 d)}{6 c}$

Step 8

Simplify the numerator.

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Step 8.1

Apply the distributive property.

$\frac{c \cdot 3 - 7 d \cdot 3 - (5 c - 8 d)}{6 c}$

Step 8.2

Move $3$ to the left of $c$ .

$\frac{3 \cdot c - 7 d \cdot 3 - (5 c - 8 d)}{6 c}$

Step 8.3

Multiply $3$ by $- 7$ .

$\frac{3 \cdot c - 21 d - (5 c - 8 d)}{6 c}$

Step 8.4

Apply the distributive property.

$\frac{3 c - 21 d - (5 c) - (- 8 d)}{6 c}$

Step 8.5

Multiply $5$ by $- 1$ .

$\frac{3 c - 21 d - 5 c - (- 8 d)}{6 c}$

Step 8.6

Multiply $- 8$ by $- 1$ .

$\frac{3 c - 21 d - 5 c + 8 d}{6 c}$

Step 8.7

Subtract $5 c$ from $3 c$ .

$\frac{- 2 c - 21 d + 8 d}{6 c}$

Step 8.8

Add $- 21 d$ and $8 d$ .

$\frac{- 2 c - 13 d}{6 c}$

Step 9

Simplify with factoring out.

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Step 9.1

Factor $- 1$ out of $- 2 c$ .

$\frac{- (2 c) - 13 d}{6 c}$

Step 9.2

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

$\frac{- (2 c) - (13 d)}{6 c}$

Step 9.3

Factor $- 1$ out of $- (2 c) - (13 d)$ .

$\frac{- (2 c + 13 d)}{6 c}$

Step 9.4

Simplify the expression.

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Step 9.4.1

Rewrite $- (2 c + 13 d)$ as $- 1 (2 c + 13 d)$ .

$\frac{- 1 (2 c + 13 d)}{6 c}$

Step 9.4.2

Move the negative in front of the fraction.

$- \frac{2 c + 13 d}{6 c}$