Simplify 2/(5(x-4))+7/(x-4)

$\frac{2}{5 (x - 4)} + \frac{7}{x - 4}$

Step 1

To write $\frac{7}{x - 4}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{2}{5 (x - 4)} + \frac{7}{x - 4} \cdot \frac{5}{5}$

Step 2

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

Multiply $\frac{7}{x - 4}$ by $\frac{5}{5}$ .

$\frac{2}{5 (x - 4)} + \frac{7 \cdot 5}{(x - 4) \cdot 5}$

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

$\frac{2}{5 (x - 4)} + \frac{7 \cdot 5}{5 (x - 4)}$

Step 3

Combine the numerators over the common denominator.

$\frac{2 + 7 \cdot 5}{5 (x - 4)}$

Step 4

Simplify the numerator.

Multiply $7$ by $5$ .

$\frac{2 + 35}{5 (x - 4)}$

Add $2$ and $35$ .

$\frac{37}{5 (x - 4)}$