Pre-Algebra Examples

$\frac{4 c}{3} - \frac{6 c + 8}{5 c - 8}$

Step 1

Factor $2$ out of $6 c + 8$ .

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Step 1.1

Factor $2$ out of $6 c$ .

$\frac{4 c}{3} - \frac{2 (3 c) + 8}{5 c - 8}$

Step 1.2

Factor $2$ out of $8$ .

$\frac{4 c}{3} - \frac{2 (3 c) + 2 (4)}{5 c - 8}$

Step 1.3

Factor $2$ out of $2 (3 c) + 2 (4)$ .

$\frac{4 c}{3} - \frac{2 (3 c + 4)}{5 c - 8}$

Step 2

To write $\frac{4 c}{3}$ as a fraction with a common denominator, multiply by $\frac{5 c - 8}{5 c - 8}$ .

$\frac{4 c}{3} \cdot \frac{5 c - 8}{5 c - 8} - \frac{2 (3 c + 4)}{5 c - 8}$

Step 3

To write $- \frac{2 (3 c + 4)}{5 c - 8}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{4 c}{3} \cdot \frac{5 c - 8}{5 c - 8} - \frac{2 (3 c + 4)}{5 c - 8} \cdot \frac{3}{3}$

Step 4

Write each expression with a common denominator of $3 (5 c - 8)$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{4 c}{3}$ by $\frac{5 c - 8}{5 c - 8}$ .

$\frac{4 c (5 c - 8)}{3 (5 c - 8)} - \frac{2 (3 c + 4)}{5 c - 8} \cdot \frac{3}{3}$

Step 4.2

Multiply $\frac{2 (3 c + 4)}{5 c - 8}$ by $\frac{3}{3}$ .

$\frac{4 c (5 c - 8)}{3 (5 c - 8)} - \frac{2 (3 c + 4) \cdot 3}{(5 c - 8) \cdot 3}$

Step 4.3

Reorder the factors of $(5 c - 8) \cdot 3$ .

$\frac{4 c (5 c - 8)}{3 (5 c - 8)} - \frac{2 (3 c + 4) \cdot 3}{3 (5 c - 8)}$

Step 5

Combine the numerators over the common denominator.

$\frac{4 c (5 c - 8) - 2 (3 c + 4) \cdot 3}{3 (5 c - 8)}$

Step 6

Simplify the numerator.

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Step 6.1

Factor $2$ out of $4 c (5 c - 8) - 2 (3 c + 4) \cdot 3$ .

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Step 6.1.1

Factor $2$ out of $4 c (5 c - 8)$ .

$\frac{2 (2 c (5 c - 8)) - 2 (3 c + 4) \cdot 3}{3 (5 c - 8)}$

Step 6.1.2

Factor $2$ out of $- 2 (3 c + 4) \cdot 3$ .

$\frac{2 (2 c (5 c - 8)) + 2 (- (3 c + 4) \cdot 3)}{3 (5 c - 8)}$

Step 6.1.3

Factor $2$ out of $2 (2 c (5 c - 8)) + 2 (- (3 c + 4) \cdot 3)$ .

$\frac{2 (2 c (5 c - 8) - (3 c + 4) \cdot 3)}{3 (5 c - 8)}$

Step 6.2

Apply the distributive property.

$\frac{2 (2 c (5 c) + 2 c \cdot - 8 - (3 c + 4) \cdot 3)}{3 (5 c - 8)}$

Step 6.3

Rewrite using the commutative property of multiplication.

$\frac{2 (2 \cdot 5 c \cdot c + 2 c \cdot - 8 - (3 c + 4) \cdot 3)}{3 (5 c - 8)}$

Step 6.4

Multiply $- 8$ by $2$ .

$\frac{2 (2 \cdot 5 c \cdot c - 16 c - (3 c + 4) \cdot 3)}{3 (5 c - 8)}$

Step 6.5

Simplify each term.

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Step 6.5.1

Multiply $c$ by $c$ by adding the exponents.

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Step 6.5.1.1

Move $c$ .

$\frac{2 (2 \cdot 5 (c \cdot c) - 16 c - (3 c + 4) \cdot 3)}{3 (5 c - 8)}$

Step 6.5.1.2

Multiply $c$ by $c$ .

$\frac{2 (2 \cdot 5 c^{2} - 16 c - (3 c + 4) \cdot 3)}{3 (5 c - 8)}$

Step 6.5.2

Multiply $2$ by $5$ .

$\frac{2 (10 c^{2} - 16 c - (3 c + 4) \cdot 3)}{3 (5 c - 8)}$

Step 6.6

Apply the distributive property.

$\frac{2 (10 c^{2} - 16 c + (- (3 c) - 1 \cdot 4) \cdot 3)}{3 (5 c - 8)}$

Step 6.7

Multiply $3$ by $- 1$ .

$\frac{2 (10 c^{2} - 16 c + (- 3 c - 1 \cdot 4) \cdot 3)}{3 (5 c - 8)}$

Step 6.8

Multiply $- 1$ by $4$ .

$\frac{2 (10 c^{2} - 16 c + (- 3 c - 4) \cdot 3)}{3 (5 c - 8)}$

Step 6.9

Apply the distributive property.

$\frac{2 (10 c^{2} - 16 c - 3 c \cdot 3 - 4 \cdot 3)}{3 (5 c - 8)}$

Step 6.10

Multiply $3$ by $- 3$ .

$\frac{2 (10 c^{2} - 16 c - 9 c - 4 \cdot 3)}{3 (5 c - 8)}$

Step 6.11

Multiply $- 4$ by $3$ .

$\frac{2 (10 c^{2} - 16 c - 9 c - 12)}{3 (5 c - 8)}$

Step 6.12

Subtract $9 c$ from $- 16 c$ .

$\frac{2 (10 c^{2} - 25 c - 12)}{3 (5 c - 8)}$