Simplify (2x+5)/3-5/x

$\frac{2 x + 5}{3} - \frac{5}{x}$

Step 1

To write $\frac{2 x + 5}{3}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{2 x + 5}{3} \cdot \frac{x}{x} - \frac{5}{x}$

Step 2

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

$\frac{2 x + 5}{3} \cdot \frac{x}{x} - \frac{5}{x} \cdot \frac{3}{3}$

Step 3

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

Multiply $\frac{2 x + 5}{3}$ by $\frac{x}{x}$ .

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

Multiply $\frac{5}{x}$ by $\frac{3}{3}$ .

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

Reorder the factors of $x \cdot 3$ .

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Simplify the numerator.

Apply the distributive property.

$\frac{2 x \cdot x + 5 x - 5 \cdot 3}{3 x}$

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

Move $x$ .

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

Multiply $x$ by $x$ .

$\frac{2 x^{2} + 5 x - 5 \cdot 3}{3 x}$

Multiply $- 5$ by $3$ .

$\frac{2 x^{2} + 5 x - 15}{3 x}$