Algebra Examples

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

Step 1

To write $2 x$ as a fraction with a common denominator, multiply by $\frac{x + 3}{x + 3}$ .

$\frac{2 x (x + 3)}{x + 3} + \frac{5 x}{x + 3}$

Step 2

Combine the numerators over the common denominator.

$\frac{2 x (x + 3) + 5 x}{x + 3}$

Step 3

Simplify the numerator.

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Step 3.1

Factor $x$ out of $2 x (x + 3) + 5 x$ .

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Step 3.1.1

Factor $x$ out of $2 x (x + 3)$ .

$\frac{x (2 (x + 3)) + 5 x}{x + 3}$

Step 3.1.2

Factor $x$ out of $5 x$ .

$\frac{x (2 (x + 3)) + x \cdot 5}{x + 3}$

Step 3.1.3

Factor $x$ out of $x (2 (x + 3)) + x \cdot 5$ .

$\frac{x (2 (x + 3) + 5)}{x + 3}$

Step 3.2

Apply the distributive property.

$\frac{x (2 x + 2 \cdot 3 + 5)}{x + 3}$

Step 3.3

Multiply $2$ by $3$ .

$\frac{x (2 x + 6 + 5)}{x + 3}$

Step 3.4

Add $6$ and $5$ .

$\frac{x (2 x + 11)}{x + 3}$