Simplify 2/(x-5)+1/(3(x-5))

$\frac{2}{x - 5} + \frac{1}{3 (x - 5)}$

Step 1

To write $\frac{2}{x - 5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{2}{x - 5} \cdot \frac{3}{3} + \frac{1}{3 (x - 5)}$

Step 2

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

Multiply $\frac{2}{x - 5}$ by $\frac{3}{3}$ .

$\frac{2 \cdot 3}{(x - 5) \cdot 3} + \frac{1}{3 (x - 5)}$

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

$\frac{2 \cdot 3}{3 (x - 5)} + \frac{1}{3 (x - 5)}$

Step 3

Combine the numerators over the common denominator.

$\frac{2 \cdot 3 + 1}{3 (x - 5)}$

Step 4

Simplify the numerator.

Multiply $2$ by $3$ .

$\frac{6 + 1}{3 (x - 5)}$

Add $6$ and $1$ .

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