Simplify (1+1/x)^2

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

Step 1

Rewrite ${(1 + \frac{1}{x})}^{2}$ as $(1 + \frac{1}{x}) (1 + \frac{1}{x})$ .

$(1 + \frac{1}{x}) (1 + \frac{1}{x})$

Step 2

Expand $(1 + \frac{1}{x}) (1 + \frac{1}{x})$ using the FOIL Method.

Apply the distributive property.

$1 (1 + \frac{1}{x}) + \frac{1}{x} (1 + \frac{1}{x})$

Apply the distributive property.

$1 \cdot 1 + 1 \frac{1}{x} + \frac{1}{x} (1 + \frac{1}{x})$

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $1$ by $1$ .

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

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

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

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

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

Multiply $\frac{1}{x} \cdot \frac{1}{x}$ .

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

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

Raise $x$ to the power of $1$ .

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

Raise $x$ to the power of $1$ .

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

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Add $1$ and $1$ .

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

Add $\frac{1}{x}$ and $\frac{1}{x}$ .

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

Step 4

Combine $2$ and $\frac{1}{x}$ .

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