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

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

To write $\frac{x + 3}{x - 6}$ as a fraction with a common denominator, multiply by $\frac{x - 2}{x - 2}$ .

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

To write $\frac{1}{x - 2}$ as a fraction with a common denominator, multiply by $\frac{x - 6}{x - 6}$ .

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

Write each expression with a common denominator of $(x - 6) (x - 2)$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{x + 3}{x - 6}$ by $\frac{x - 2}{x - 2}$ .

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

Multiply $\frac{1}{x - 2}$ by $\frac{x - 6}{x - 6}$ .

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

Reorder the factors of $(x - 6) (x - 2)$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Expand $(x + 3) (x - 2)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

Move $- 2$ to the left of $x$ .

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

Multiply $3$ by $- 2$ .

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

Add $- 2 x$ and $3 x$ .

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

Add $x$ and $x$ .

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

Subtract $6$ from $- 6$ .

$\frac{x^{2} + 2 x - 12}{(x - 2) (x - 6)}$