Simplify (5x-1)/(x+3)+9/(x(x+3))

$\frac{5 x - 1}{x + 3} + \frac{9}{x (x + 3)}$

Step 1

To write $\frac{5 x - 1}{x + 3}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{5 x - 1}{x + 3} \cdot \frac{x}{x} + \frac{9}{x (x + 3)}$

Step 2

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

Multiply $\frac{5 x - 1}{x + 3}$ by $\frac{x}{x}$ .

$\frac{(5 x - 1) x}{(x + 3) x} + \frac{9}{x (x + 3)}$

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

$\frac{(5 x - 1) x}{x (x + 3)} + \frac{9}{x (x + 3)}$

Step 3

Combine the numerators over the common denominator.

$\frac{(5 x - 1) x + 9}{x (x + 3)}$

Step 4

Simplify the numerator.

Apply the distributive property.

$\frac{5 x \cdot x - 1 x + 9}{x (x + 3)}$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$\frac{5 (x \cdot x) - 1 x + 9}{x (x + 3)}$

Multiply $x$ by $x$ .

$\frac{5 x^{2} - 1 x + 9}{x (x + 3)}$

Rewrite $- 1 x$ as $- x$ .

$\frac{5 x^{2} - x + 9}{x (x + 3)}$