Algebra Examples

$\frac{3}{x} - 2 - \frac{5}{x}$

Step 1

Combine the numerators over the common denominator.

$- 2 + \frac{3 - 5}{x}$

Step 2

Simplify the expression.

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Step 2.1

Subtract $5$ from $3$ .

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

Step 2.2

Move the negative in front of the fraction.

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

Step 3

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

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

Step 4

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

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

Step 5

Combine the numerators over the common denominator.

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

Step 6

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

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Step 6.1

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

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

Step 6.2

Factor $2$ out of $- 2$ .

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

Step 6.3

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

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

Step 7

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

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

Step 8

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

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

Step 9

Factor $- 1$ out of $- (x) - 1 (1)$ .

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

Step 10

Simplify the expression.

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Step 10.1

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

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

Step 10.2

Move the negative in front of the fraction.

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