Simplify x/y-1/(xy)

$\frac{x}{y} - \frac{1}{x y}$

Step 1

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

$\frac{x}{y} \cdot \frac{x}{x} - \frac{1}{x y}$

Step 2

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

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

$\frac{x \cdot x}{y x} - \frac{1}{x y}$

Reorder the factors of $y x$ .

$\frac{x \cdot x}{x y} - \frac{1}{x y}$

Step 3

Combine the numerators over the common denominator.

$\frac{x \cdot x - 1}{x y}$

Step 4

Simplify the numerator.

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

$\frac{x^{1} x - 1}{x y}$

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

$\frac{x^{1} x^{1} - 1}{x y}$

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

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

Add $1$ and $1$ .

$\frac{x^{2} - 1}{x y}$

Rewrite $1$ as $1^{2}$ .

$\frac{x^{2} - 1^{2}}{x y}$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 1$ .

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