Basic Math Examples

$- \frac{8 c - d}{6 c} + \frac{9 c + 8 d}{4 c} + 1$

Step 1

To write $- \frac{8 c - d}{6 c}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{8 c - d}{6 c} \cdot \frac{2}{2} + \frac{9 c + 8 d}{4 c} + 1$

Step 2

To write $\frac{9 c + 8 d}{4 c}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{8 c - d}{6 c} \cdot \frac{2}{2} + \frac{9 c + 8 d}{4 c} \cdot \frac{3}{3} + 1$

Step 3

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

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Step 3.1

Multiply $\frac{8 c - d}{6 c}$ by $\frac{2}{2}$ .

$- \frac{(8 c - d) \cdot 2}{6 c \cdot 2} + \frac{9 c + 8 d}{4 c} \cdot \frac{3}{3} + 1$

Step 3.2

Multiply $2$ by $6$ .

$- \frac{(8 c - d) \cdot 2}{12 c} + \frac{9 c + 8 d}{4 c} \cdot \frac{3}{3} + 1$

Step 3.3

Multiply $\frac{9 c + 8 d}{4 c}$ by $\frac{3}{3}$ .

$- \frac{(8 c - d) \cdot 2}{12 c} + \frac{(9 c + 8 d) \cdot 3}{4 c \cdot 3} + 1$

Step 3.4

Multiply $3$ by $4$ .

$- \frac{(8 c - d) \cdot 2}{12 c} + \frac{(9 c + 8 d) \cdot 3}{12 c} + 1$

Step 4

Combine the numerators over the common denominator.

$\frac{- (8 c - d) \cdot 2 + (9 c + 8 d) \cdot 3}{12 c} + 1$

Step 5

Simplify the numerator.

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Step 5.1

Apply the distributive property.

$\frac{(- (8 c) - - d) \cdot 2 + (9 c + 8 d) \cdot 3}{12 c} + 1$

Step 5.2

Multiply $8$ by $- 1$ .

$\frac{(- 8 c - - d) \cdot 2 + (9 c + 8 d) \cdot 3}{12 c} + 1$

Step 5.3

Multiply $- - d$ .

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Step 5.3.1

Multiply $- 1$ by $- 1$ .

$\frac{(- 8 c + 1 d) \cdot 2 + (9 c + 8 d) \cdot 3}{12 c} + 1$

Step 5.3.2

Multiply $d$ by $1$ .

$\frac{(- 8 c + d) \cdot 2 + (9 c + 8 d) \cdot 3}{12 c} + 1$

Step 5.4

Apply the distributive property.

$\frac{- 8 c \cdot 2 + d \cdot 2 + (9 c + 8 d) \cdot 3}{12 c} + 1$

Step 5.5

Multiply $2$ by $- 8$ .

$\frac{- 16 c + d \cdot 2 + (9 c + 8 d) \cdot 3}{12 c} + 1$

Step 5.6

Move $2$ to the left of $d$ .

$\frac{- 16 c + 2 \cdot d + (9 c + 8 d) \cdot 3}{12 c} + 1$

Step 5.7

Apply the distributive property.

$\frac{- 16 c + 2 d + 9 c \cdot 3 + 8 d \cdot 3}{12 c} + 1$

Step 5.8

Multiply $3$ by $9$ .

$\frac{- 16 c + 2 d + 27 c + 8 d \cdot 3}{12 c} + 1$

Step 5.9

Multiply $3$ by $8$ .

$\frac{- 16 c + 2 d + 27 c + 24 d}{12 c} + 1$

Step 5.10

Add $- 16 c$ and $27 c$ .

$\frac{11 c + 2 d + 24 d}{12 c} + 1$

Step 5.11

Add $2 d$ and $24 d$ .

$\frac{11 c + 26 d}{12 c} + 1$

Step 6

Simplify terms.

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Step 6.1

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

$\frac{11 c + 26 d}{12 c} + \frac{12 c}{12 c}$

Step 6.2

Combine the numerators over the common denominator.

$\frac{11 c + 26 d + 12 c}{12 c}$

Step 6.3

Add $11 c$ and $12 c$ .

$\frac{23 c + 26 d}{12 c}$