Algebra Examples

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

Step 1

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

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

Step 2

Combine the numerators over the common denominator.

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

Step 3

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

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

Step 4

Combine $- x$ and $\frac{x}{x}$ .

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

Step 5

Combine the numerators over the common denominator.

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

Step 6

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

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Step 6.1

Move $x$ .

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

Step 6.2

Multiply $x$ by $x$ .

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

Step 7

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

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

Step 8

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

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

Step 9

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

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

Step 10

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

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

Step 11

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

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

Step 12

Simplify the expression.

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Step 12.1

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

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

Step 12.2

Move the negative in front of the fraction.

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