Pre-Algebra Examples

$\frac{x + 2}{3 x} + \frac{x + 5}{2 x^{2} + 10 x}$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Factor $2 x$ out of $2 x^{2} + 10 x$ .

Tap for more steps...

Step 1.1.1

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

$\frac{x + 2}{3 x} + \frac{x + 5}{2 x (x) + 10 x}$

Step 1.1.2

Factor $2 x$ out of $10 x$ .

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

Step 1.1.3

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

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

Step 1.2

Cancel the common factor of $x + 5$ .

Tap for more steps...

Step 1.2.1

Cancel the common factor.

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

Step 1.2.2

Rewrite the expression.

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

Step 2

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

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

Step 3

To write $\frac{1}{2 x}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 4

Write each expression with a common denominator of $6 x$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 4.1

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

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

Step 4.2

Multiply $2$ by $3$ .

$\frac{(x + 2) \cdot 2}{6 x} + \frac{1}{2 x} \cdot \frac{3}{3}$

Step 4.3

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

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

Step 4.4

Multiply $3$ by $2$ .

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

Step 5

Combine the numerators over the common denominator.

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

Step 6

Simplify the numerator.

Tap for more steps...

Step 6.1

Apply the distributive property.

$\frac{x \cdot 2 + 2 \cdot 2 + 3}{6 x}$

Step 6.2

Move $2$ to the left of $x$ .

$\frac{2 \cdot x + 2 \cdot 2 + 3}{6 x}$

Step 6.3

Multiply $2$ by $2$ .

$\frac{2 \cdot x + 4 + 3}{6 x}$

Step 6.4

Add $4$ and $3$ .

$\frac{2 x + 7}{6 x}$