Simplify (2x+1)/x+3/(x^2)

$\frac{2 x + 1}{x} + \frac{3}{x^{2}}$

Step 1

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

$\frac{2 x + 1}{x} \cdot \frac{x}{x} + \frac{3}{x^{2}}$

Step 2

Write each expression with a common denominator of $x^{2}$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{2 x + 1}{x}$ by $\frac{x}{x}$ .

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

Multiply $x$ by $x$ .

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

Step 3

Combine the numerators over the common denominator.

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

Step 4

Simplify the numerator.

Apply the distributive property.

$\frac{2 x \cdot x + 1 x + 3}{x^{2}}$

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

Move $x$ .

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

Multiply $x$ by $x$ .

$\frac{2 x^{2} + 1 x + 3}{x^{2}}$

Multiply $x$ by $1$ .

$\frac{2 x^{2} + x + 3}{x^{2}}$