Basic Math Examples

$\frac{5}{k + 3} + \frac{7}{k}$

Step 1

To write $\frac{5}{k + 3}$ as a fraction with a common denominator, multiply by $\frac{k}{k}$ .

$\frac{5}{k + 3} \cdot \frac{k}{k} + \frac{7}{k}$

Step 2

To write $\frac{7}{k}$ as a fraction with a common denominator, multiply by $\frac{k + 3}{k + 3}$ .

$\frac{5}{k + 3} \cdot \frac{k}{k} + \frac{7}{k} \cdot \frac{k + 3}{k + 3}$

Step 3

Write each expression with a common denominator of $(k + 3) k$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 3.1

Multiply $\frac{5}{k + 3}$ by $\frac{k}{k}$ .

$\frac{5 k}{(k + 3) k} + \frac{7}{k} \cdot \frac{k + 3}{k + 3}$

Step 3.2

Multiply $\frac{7}{k}$ by $\frac{k + 3}{k + 3}$ .

$\frac{5 k}{(k + 3) k} + \frac{7 (k + 3)}{k (k + 3)}$

Step 3.3

Reorder the factors of $(k + 3) k$ .

$\frac{5 k}{k (k + 3)} + \frac{7 (k + 3)}{k (k + 3)}$

Step 4

Combine the numerators over the common denominator.

$\frac{5 k + 7 (k + 3)}{k (k + 3)}$

Step 5

Simplify the numerator.

Tap for more steps...

Step 5.1

Apply the distributive property.

$\frac{5 k + 7 k + 7 \cdot 3}{k (k + 3)}$

Step 5.2

Multiply $7$ by $3$ .

$\frac{5 k + 7 k + 21}{k (k + 3)}$

Step 5.3

Add $5 k$ and $7 k$ .

$\frac{12 k + 21}{k (k + 3)}$

Step 5.4

Factor $3$ out of $12 k + 21$ .

Tap for more steps...

Step 5.4.1

Factor $3$ out of $12 k$ .

$\frac{3 (4 k) + 21}{k (k + 3)}$

Step 5.4.2

Factor $3$ out of $21$ .

$\frac{3 (4 k) + 3 (7)}{k (k + 3)}$

Step 5.4.3

Factor $3$ out of $3 (4 k) + 3 (7)$ .

$\frac{3 (4 k + 7)}{k (k + 3)}$