Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Multiply $- 1$ by $3$ .

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

Step 2

Find the common denominator.

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Step 2.1

Write $- x$ as a fraction with denominator $1$ .

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

Step 2.2

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

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

Step 2.3

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

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

Step 2.4

Write $- 3$ as a fraction with denominator $1$ .

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

Step 2.5

Multiply $\frac{- 3}{1}$ by $\frac{x}{x}$ .

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

Step 2.6

Multiply $\frac{- 3}{1}$ by $\frac{x}{x}$ .

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

Step 3

Combine the numerators over the common denominator.

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

Step 4

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

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Step 4.1

Move $x$ .

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

Step 4.2

Multiply $x$ by $x$ .

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

Step 5

Subtract $3 x$ from $x$ .

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

Step 6

Reorder terms.

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

Step 7

Factor $- 1$ out of $- x^{2}$ .

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

Step 8

Factor $- 1$ out of $- 2 x$ .

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

Step 9

Factor $- 1$ out of $- (x^{2}) - (2 x)$ .

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

Step 10

Rewrite $2$ as $- 1 (- 2)$ .

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

Step 11

Factor $- 1$ out of $- (x^{2} + 2 x) - 1 (- 2)$ .

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

Step 12

Simplify the expression.

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Step 12.1

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

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

Step 12.2

Move the negative in front of the fraction.

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