Calculus Examples

$\frac{4}{5 (k - 3)} + \frac{5}{2 (k - 3)}$

Step 1

To write $\frac{4}{5 (k - 3)}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{4}{5 (k - 3)} \cdot \frac{2}{2} + \frac{5}{2 (k - 3)}$

Step 2

To write $\frac{5}{2 (k - 3)}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{4}{5 (k - 3)} \cdot \frac{2}{2} + \frac{5}{2 (k - 3)} \cdot \frac{5}{5}$

Step 3

Write each expression with a common denominator of $10 (k - 3)$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{4}{5 (k - 3)}$ by $\frac{2}{2}$ .

$\frac{4 \cdot 2}{5 (k - 3) \cdot 2} + \frac{5}{2 (k - 3)} \cdot \frac{5}{5}$

Step 3.2

Multiply $2$ by $5$ .

$\frac{4 \cdot 2}{10 (k - 3)} + \frac{5}{2 (k - 3)} \cdot \frac{5}{5}$

Step 3.3

Multiply $\frac{5}{2 (k - 3)}$ by $\frac{5}{5}$ .

$\frac{4 \cdot 2}{10 (k - 3)} + \frac{5 \cdot 5}{2 (k - 3) \cdot 5}$

Step 3.4

Multiply $5$ by $2$ .

$\frac{4 \cdot 2}{10 (k - 3)} + \frac{5 \cdot 5}{10 (k - 3)}$

Step 4

Combine the numerators over the common denominator.

$\frac{4 \cdot 2 + 5 \cdot 5}{10 (k - 3)}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $4$ by $2$ .

$\frac{8 + 5 \cdot 5}{10 (k - 3)}$

Step 5.2

Multiply $5$ by $5$ .

$\frac{8 + 25}{10 (k - 3)}$

Step 5.3

Add $8$ and $25$ .

$\frac{33}{10 (k - 3)}$