Simplify 4/(x^2-3x)+6/(3x-9)

$\frac{4}{x^{2} - 3 x} + \frac{6}{3 x - 9}$

Step 1

Simplify each term.

Factor $x$ out of $x^{2} - 3 x$ .

Factor $x$ out of $x^{2}$ .

$\frac{4}{x \cdot x - 3 x} + \frac{6}{3 x - 9}$

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

$\frac{4}{x \cdot x + x \cdot - 3} + \frac{6}{3 x - 9}$

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

$\frac{4}{x (x - 3)} + \frac{6}{3 x - 9}$

Cancel the common factor of $6$ and $3 x - 9$ .

Factor $3$ out of $6$ .

$\frac{4}{x (x - 3)} + \frac{3 \cdot 2}{3 x - 9}$

Cancel the common factors.

Factor $3$ out of $3 x$ .

$\frac{4}{x (x - 3)} + \frac{3 \cdot 2}{3 (x) - 9}$

Factor $3$ out of $- 9$ .

$\frac{4}{x (x - 3)} + \frac{3 \cdot 2}{3 (x) + 3 (- 3)}$

Factor $3$ out of $3 (x) + 3 (- 3)$ .

$\frac{4}{x (x - 3)} + \frac{3 \cdot 2}{3 (x - 3)}$

Cancel the common factor.

$\frac{4}{x (x - 3)} + \frac{3 \cdot 2}{3 (x - 3)}$

Rewrite the expression.

$\frac{4}{x (x - 3)} + \frac{2}{x - 3}$

Step 2

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

$\frac{4}{x (x - 3)} + \frac{2}{x - 3} \cdot \frac{x}{x}$

Step 3

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

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

$\frac{4}{x (x - 3)} + \frac{2 x}{(x - 3) x}$

Reorder the factors of $(x - 3) x$ .

$\frac{4}{x (x - 3)} + \frac{2 x}{x (x - 3)}$

Step 4

Combine the numerators over the common denominator.

$\frac{4 + 2 x}{x (x - 3)}$

Step 5

Factor $2$ out of $4 + 2 x$ .

Factor $2$ out of $4$ .

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

Factor $2$ out of $2 \cdot 2 + 2 x$ .

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