Algebra Examples

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

Step 1

To write $2$ as a fraction with a common denominator, multiply by $\frac{x + 1}{x + 1}$ .

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

Step 2

Combine the numerators over the common denominator.

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

Step 3

Simplify the numerator.

Tap for more steps...

Step 3.1

Apply the distributive property.

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

Step 3.2

Multiply $2$ by $1$ .

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

Step 3.3

Add $2$ and $1$ .

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

Step 4

Simplify terms.

Tap for more steps...

Step 4.1

Cancel the common factor of $x + 1$ .

Tap for more steps...

Step 4.1.1

Cancel the common factor.

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

Step 4.1.2

Rewrite the expression.

$\frac{1}{x} (2 x + 3)$

Step 4.2

Multiply $\frac{1}{x}$ by $2 x + 3$ .

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