Basic Math Examples

$\frac{6 π}{15 π - 15} + \frac{2 π}{3}$

Step 1

Cancel the common factor of $6$ and $15 π - 15$ .

Tap for more steps...

Step 1.1

Factor $3$ out of $6 π$ .

$\frac{3 (2 π)}{15 π - 15} + \frac{2 π}{3}$

Step 1.2

Cancel the common factors.

Tap for more steps...

Step 1.2.1

Factor $3$ out of $15 π$ .

$\frac{3 (2 π)}{3 (5 π) - 15} + \frac{2 π}{3}$

Step 1.2.2

Factor $3$ out of $- 15$ .

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

Step 1.2.3

Factor $3$ out of $3 (5 π) + 3 (- 5)$ .

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

Step 1.2.4

Cancel the common factor.

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

Step 1.2.5

Rewrite the expression.

$\frac{2 π}{5 π - 5} + \frac{2 π}{3}$

Step 2

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

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

Step 3

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

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

Step 4

Write each expression with a common denominator of $(5 π - 5) \cdot 3$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 4.1

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

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

Step 4.2

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

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

Step 4.3

Reorder the factors of $(5 π - 5) \cdot 3$ .

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

Step 5

Combine the numerators over the common denominator.

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

Step 6

Simplify the numerator.

Tap for more steps...

Step 6.1

Factor $2 π$ out of $2 π \cdot 3 + 2 π (5 π - 5)$ .

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

Step 6.2

Subtract $5$ from $3$ .

$\frac{2 π (5 π - 2)}{3 (5 π - 5)}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{2 π (5 π - 2)}{3 (5 π - 5)}$

Decimal Form:

$2.68117198 \dots$