Algebra Examples

$\frac{3 c}{c - 4} - \frac{2}{5}$

Step 1

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

$\frac{3 c}{c - 4} \cdot \frac{5}{5} - \frac{2}{5}$

Step 2

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

$\frac{3 c}{c - 4} \cdot \frac{5}{5} - \frac{2}{5} \cdot \frac{c - 4}{c - 4}$

Step 3

Write each expression with a common denominator of $(c - 4) \cdot 5$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

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

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

Step 3.2

Multiply $\frac{2}{5}$ by $\frac{c - 4}{c - 4}$ .

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

Step 3.3

Reorder the factors of $(c - 4) \cdot 5$ .

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Simplify the numerator.

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Step 5.1

Multiply $5$ by $3$ .

$\frac{15 c - 2 (c - 4)}{5 (c - 4)}$

Step 5.2

Apply the distributive property.

$\frac{15 c - 2 c - 2 \cdot - 4}{5 (c - 4)}$

Step 5.3

Multiply $- 2$ by $- 4$ .

$\frac{15 c - 2 c + 8}{5 (c - 4)}$

Step 5.4

Subtract $2 c$ from $15 c$ .

$\frac{13 c + 8}{5 (c - 4)}$