Simplify 1/x+(5x)/(x+8)

$\frac{1}{x} + \frac{5 x}{x + 8}$

Step 1

To write $\frac{1}{x}$ as a fraction with a common denominator, multiply by $\frac{x + 8}{x + 8}$ .

$\frac{1}{x} \cdot \frac{x + 8}{x + 8} + \frac{5 x}{x + 8}$

Step 2

To write $\frac{5 x}{x + 8}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{1}{x} \cdot \frac{x + 8}{x + 8} + \frac{5 x}{x + 8} \cdot \frac{x}{x}$

Step 3

Write each expression with a common denominator of $x (x + 8)$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{x}$ by $\frac{x + 8}{x + 8}$ .

$\frac{x + 8}{x (x + 8)} + \frac{5 x}{x + 8} \cdot \frac{x}{x}$

Multiply $\frac{5 x}{x + 8}$ by $\frac{x}{x}$ .

$\frac{x + 8}{x (x + 8)} + \frac{5 x \cdot x}{(x + 8) x}$

Reorder the factors of $(x + 8) x$ .

$\frac{x + 8}{x (x + 8)} + \frac{5 x \cdot x}{x (x + 8)}$

Step 4

Combine the numerators over the common denominator.

$\frac{x + 8 + 5 x \cdot x}{x (x + 8)}$

Step 5

Simplify the numerator.

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

Move $x$ .

$\frac{x + 8 + 5 (x \cdot x)}{x (x + 8)}$

Multiply $x$ by $x$ .

$\frac{x + 8 + 5 x^{2}}{x (x + 8)}$

Reorder terms.

$\frac{5 x^{2} + x + 8}{x (x + 8)}$