Simplify (2x)/(3x-18)+(x+1)/(x-6)

$\frac{2 x}{3 x - 18} + \frac{x + 1}{x - 6}$

Step 1

Factor $3$ out of $3 x - 18$ .

Factor $3$ out of $3 x$ .

$\frac{2 x}{3 (x) - 18} + \frac{x + 1}{x - 6}$

Factor $3$ out of $- 18$ .

$\frac{2 x}{3 x + 3 \cdot - 6} + \frac{x + 1}{x - 6}$

Factor $3$ out of $3 x + 3 \cdot - 6$ .

$\frac{2 x}{3 (x - 6)} + \frac{x + 1}{x - 6}$

Step 2

To write $\frac{x + 1}{x - 6}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{2 x}{3 (x - 6)} + \frac{x + 1}{x - 6} \cdot \frac{3}{3}$

Step 3

Write each expression with a common denominator of $3 (x - 6)$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{x + 1}{x - 6}$ by $\frac{3}{3}$ .

$\frac{2 x}{3 (x - 6)} + \frac{(x + 1) \cdot 3}{(x - 6) \cdot 3}$

Reorder the factors of $(x - 6) \cdot 3$ .

$\frac{2 x}{3 (x - 6)} + \frac{(x + 1) \cdot 3}{3 (x - 6)}$

Step 4

Combine the numerators over the common denominator.

$\frac{2 x + (x + 1) \cdot 3}{3 (x - 6)}$

Step 5

Simplify the numerator.

Apply the distributive property.

$\frac{2 x + x \cdot 3 + 1 \cdot 3}{3 (x - 6)}$

Move $3$ to the left of $x$ .

$\frac{2 x + 3 \cdot x + 1 \cdot 3}{3 (x - 6)}$

Multiply $3$ by $1$ .

$\frac{2 x + 3 \cdot x + 3}{3 (x - 6)}$

Add $2 x$ and $3 x$ .

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