Basic Math Examples

$3 - \sqrt{5} \div 3 + \sqrt{5} \cdot 3 - \sqrt{5} \div 3 - \sqrt{5}$

Step 1

Combine the numerators over the common denominator.

$3 + \sqrt{5} \cdot 3 - \sqrt{5} + \frac{- \sqrt{5} - \sqrt{5}}{3}$

Step 2

Subtract $\sqrt{5}$ from $- \sqrt{5}$ .

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

Step 3

Find the common denominator.

Tap for more steps...

Step 3.1

Write $3$ as a fraction with denominator $1$ .

$\frac{3}{1} + \sqrt{5} \cdot 3 - \sqrt{5} + \frac{- 2 \sqrt{5}}{3}$

Step 3.2

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

$\frac{3}{1} \cdot \frac{3}{3} + \sqrt{5} \cdot 3 - \sqrt{5} + \frac{- 2 \sqrt{5}}{3}$

Step 3.3

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

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

Step 3.4

Write $\sqrt{5} \cdot 3$ as a fraction with denominator $1$ .

$\frac{3 \cdot 3}{3} + \frac{\sqrt{5} \cdot 3}{1} - \sqrt{5} + \frac{- 2 \sqrt{5}}{3}$

Step 3.5

Multiply $\frac{\sqrt{5} \cdot 3}{1}$ by $\frac{3}{3}$ .

$\frac{3 \cdot 3}{3} + \frac{\sqrt{5} \cdot 3}{1} \cdot \frac{3}{3} - \sqrt{5} + \frac{- 2 \sqrt{5}}{3}$

Step 3.6

Multiply $\frac{\sqrt{5} \cdot 3}{1}$ by $\frac{3}{3}$ .

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

Step 3.7

Write $- \sqrt{5}$ as a fraction with denominator $1$ .

$\frac{3 \cdot 3}{3} + \frac{\sqrt{5} \cdot 3 \cdot 3}{3} + \frac{- \sqrt{5}}{1} + \frac{- 2 \sqrt{5}}{3}$

Step 3.8

Multiply $\frac{- \sqrt{5}}{1}$ by $\frac{3}{3}$ .

$\frac{3 \cdot 3}{3} + \frac{\sqrt{5} \cdot 3 \cdot 3}{3} + \frac{- \sqrt{5}}{1} \cdot \frac{3}{3} + \frac{- 2 \sqrt{5}}{3}$

Step 3.9

Multiply $\frac{- \sqrt{5}}{1}$ by $\frac{3}{3}$ .

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Simplify each term.

Tap for more steps...

Step 5.1

Multiply $3$ by $3$ .

$\frac{9 + \sqrt{5} \cdot 3 \cdot 3 - \sqrt{5} \cdot 3 - 2 \sqrt{5}}{3}$

Step 5.2

Move $3$ to the left of $\sqrt{5}$ .

$\frac{9 + 3 \cdot \sqrt{5} \cdot 3 - \sqrt{5} \cdot 3 - 2 \sqrt{5}}{3}$

Step 5.3

Multiply $3$ by $3$ .

$\frac{9 + 9 \sqrt{5} - \sqrt{5} \cdot 3 - 2 \sqrt{5}}{3}$

Step 5.4

Multiply $3$ by $- 1$ .

$\frac{9 + 9 \sqrt{5} - 3 \sqrt{5} - 2 \sqrt{5}}{3}$

Step 6

Simplify by adding terms.

Tap for more steps...

Step 6.1

Subtract $3 \sqrt{5}$ from $9 \sqrt{5}$ .

$\frac{9 + 6 \sqrt{5} - 2 \sqrt{5}}{3}$

Step 6.2

Subtract $2 \sqrt{5}$ from $6 \sqrt{5}$ .

$\frac{9 + 4 \sqrt{5}}{3}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{9 + 4 \sqrt{5}}{3}$

Decimal Form:

$5.98142397 \dots$