Basic Math Examples

$\frac{5}{2} + \frac{4 d}{3 d + 18}$

Step 1

Factor $3$ out of $3 d + 18$ .

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Step 1.1

Factor $3$ out of $3 d$ .

$\frac{5}{2} + \frac{4 d}{3 (d) + 18}$

Step 1.2

Factor $3$ out of $18$ .

$\frac{5}{2} + \frac{4 d}{3 d + 3 \cdot 6}$

Step 1.3

Factor $3$ out of $3 d + 3 \cdot 6$ .

$\frac{5}{2} + \frac{4 d}{3 (d + 6)}$

Step 2

To write $\frac{5}{2}$ as a fraction with a common denominator, multiply by $\frac{3 (d + 6)}{3 (d + 6)}$ .

$\frac{5}{2} \cdot \frac{3 (d + 6)}{3 (d + 6)} + \frac{4 d}{3 (d + 6)}$

Step 3

To write $\frac{4 d}{3 (d + 6)}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{5}{2} \cdot \frac{3 (d + 6)}{3 (d + 6)} + \frac{4 d}{3 (d + 6)} \cdot \frac{2}{2}$

Step 4

Write each expression with a common denominator of $6 (d + 6)$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{5}{2}$ by $\frac{3 (d + 6)}{3 (d + 6)}$ .

$\frac{5 (3 (d + 6))}{2 (3 (d + 6))} + \frac{4 d}{3 (d + 6)} \cdot \frac{2}{2}$

Step 4.2

Multiply $3$ by $2$ .

$\frac{5 (3 (d + 6))}{6 (d + 6)} + \frac{4 d}{3 (d + 6)} \cdot \frac{2}{2}$

Step 4.3

Multiply $\frac{4 d}{3 (d + 6)}$ by $\frac{2}{2}$ .

$\frac{5 (3 (d + 6))}{6 (d + 6)} + \frac{4 d \cdot 2}{3 (d + 6) \cdot 2}$

Step 4.4

Multiply $2$ by $3$ .

$\frac{5 (3 (d + 6))}{6 (d + 6)} + \frac{4 d \cdot 2}{6 (d + 6)}$

Step 5

Combine the numerators over the common denominator.

$\frac{5 (3 (d + 6)) + 4 d \cdot 2}{6 (d + 6)}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $5$ by $3$ .

$\frac{15 (d + 6) + 4 d \cdot 2}{6 (d + 6)}$

Step 6.2

Apply the distributive property.

$\frac{15 d + 15 \cdot 6 + 4 d \cdot 2}{6 (d + 6)}$

Step 6.3

Multiply $15$ by $6$ .

$\frac{15 d + 90 + 4 d \cdot 2}{6 (d + 6)}$

Step 6.4

Multiply $2$ by $4$ .

$\frac{15 d + 90 + 8 d}{6 (d + 6)}$

Step 6.5

Add $15 d$ and $8 d$ .

$\frac{23 d + 90}{6 (d + 6)}$