Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Rewrite using the commutative property of multiplication.

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

Step 1.3

Cancel the common factor of $x$ .

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Step 1.3.1

Factor $x$ out of $- x$ .

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

Step 1.3.2

Cancel the common factor.

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

Step 1.3.3

Rewrite the expression.

$x y - 1 - x y$

Step 2

Combine the opposite terms in $x y - 1 - x y$ .

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Step 2.1

Subtract $x y$ from $x y$ .

$0 - 1$

Step 2.2

Subtract $1$ from $0$ .

$- 1$