Basic Math Examples

$\frac{v}{2} + \frac{v - 5}{v + 3}$

Step 1

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

$\frac{v}{2} \cdot \frac{v + 3}{v + 3} + \frac{v - 5}{v + 3}$

Step 2

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

$\frac{v}{2} \cdot \frac{v + 3}{v + 3} + \frac{v - 5}{v + 3} \cdot \frac{2}{2}$

Step 3

Write each expression with a common denominator of $2 (v + 3)$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

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

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

Step 3.2

Multiply $\frac{v - 5}{v + 3}$ by $\frac{2}{2}$ .

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

Step 3.3

Reorder the factors of $(v + 3) \cdot 2$ .

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Simplify the numerator.

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Step 5.1

Apply the distributive property.

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

Step 5.2

Multiply $v$ by $v$ .

$\frac{v^{2} + v \cdot 3 + (v - 5) \cdot 2}{2 (v + 3)}$

Step 5.3

Move $3$ to the left of $v$ .

$\frac{v^{2} + 3 \cdot v + (v - 5) \cdot 2}{2 (v + 3)}$

Step 5.4

Apply the distributive property.

$\frac{v^{2} + 3 v + v \cdot 2 - 5 \cdot 2}{2 (v + 3)}$

Step 5.5

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

$\frac{v^{2} + 3 v + 2 \cdot v - 5 \cdot 2}{2 (v + 3)}$

Step 5.6

Multiply $- 5$ by $2$ .

$\frac{v^{2} + 3 v + 2 \cdot v - 10}{2 (v + 3)}$

Step 5.7

Add $3 v$ and $2 v$ .

$\frac{v^{2} + 5 v - 10}{2 (v + 3)}$