Algebra Examples

$\frac{1}{x - 4} + \frac{3}{5}$

Step 1

To write $\frac{1}{x - 4}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{1}{x - 4} \cdot \frac{5}{5} + \frac{3}{5}$

Step 2

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

$\frac{1}{x - 4} \cdot \frac{5}{5} + \frac{3}{5} \cdot \frac{x - 4}{x - 4}$

Step 3

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

Tap for more steps...

Step 3.1

Multiply $\frac{1}{x - 4}$ by $\frac{5}{5}$ .

$\frac{5}{(x - 4) \cdot 5} + \frac{3}{5} \cdot \frac{x - 4}{x - 4}$

Step 3.2

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

$\frac{5}{(x - 4) \cdot 5} + \frac{3 (x - 4)}{5 (x - 4)}$

Step 3.3

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

$\frac{5}{5 (x - 4)} + \frac{3 (x - 4)}{5 (x - 4)}$

Step 4

Combine the numerators over the common denominator.

$\frac{5 + 3 (x - 4)}{5 (x - 4)}$

Step 5

Simplify the numerator.

Tap for more steps...

Step 5.1

Apply the distributive property.

$\frac{5 + 3 x + 3 \cdot - 4}{5 (x - 4)}$

Step 5.2

Multiply $3$ by $- 4$ .

$\frac{5 + 3 x - 12}{5 (x - 4)}$

Step 5.3

Subtract $12$ from $5$ .

$\frac{3 x - 7}{5 (x - 4)}$