Basic Math Examples

$\frac{v - 1}{10 v^{2} - 6 v} + \frac{3 v}{2}$

Step 1

Factor $2 v$ out of $10 v^{2} - 6 v$ .

Tap for more steps...

Step 1.1

Factor $2 v$ out of $10 v^{2}$ .

$\frac{v - 1}{2 v (5 v) - 6 v} + \frac{3 v}{2}$

Step 1.2

Factor $2 v$ out of $- 6 v$ .

$\frac{v - 1}{2 v (5 v) + 2 v (- 3)} + \frac{3 v}{2}$

Step 1.3

Factor $2 v$ out of $2 v (5 v) + 2 v (- 3)$ .

$\frac{v - 1}{2 v (5 v - 3)} + \frac{3 v}{2}$

Step 2

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

$\frac{v - 1}{2 v (5 v - 3)} + \frac{3 v}{2} \cdot \frac{v (5 v - 3)}{v (5 v - 3)}$

Step 3

Write each expression with a common denominator of $2 v (5 v - 3)$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 3.1

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

$\frac{v - 1}{2 v (5 v - 3)} + \frac{3 v (v (5 v - 3))}{2 (v (5 v - 3))}$

Step 3.2

Reorder the factors of $2 (v (5 v - 3))$ .

$\frac{v - 1}{2 v (5 v - 3)} + \frac{3 v (v (5 v - 3))}{2 v (5 v - 3)}$

Step 4

Combine the numerators over the common denominator.

$\frac{v - 1 + 3 v (v (5 v - 3))}{2 v (5 v - 3)}$

Step 5

Simplify the numerator.

Tap for more steps...

Step 5.1

Multiply $v$ by $v$ by adding the exponents.

Tap for more steps...

Step 5.1.1

Move $v$ .

$\frac{v - 1 + 3 (v \cdot v) (5 v - 3)}{2 v (5 v - 3)}$

Step 5.1.2

Multiply $v$ by $v$ .

$\frac{v - 1 + 3 v^{2} (5 v - 3)}{2 v (5 v - 3)}$

Step 5.2

Apply the distributive property.

$\frac{v - 1 + 3 v^{2} (5 v) + 3 v^{2} \cdot - 3}{2 v (5 v - 3)}$

Step 5.3

Rewrite using the commutative property of multiplication.

$\frac{v - 1 + 3 \cdot 5 v^{2} v + 3 v^{2} \cdot - 3}{2 v (5 v - 3)}$

Step 5.4

Multiply $- 3$ by $3$ .

$\frac{v - 1 + 3 \cdot 5 v^{2} v - 9 v^{2}}{2 v (5 v - 3)}$

Step 5.5

Simplify each term.

Tap for more steps...

Step 5.5.1

Multiply $v^{2}$ by $v$ by adding the exponents.

Tap for more steps...

Step 5.5.1.1

Move $v$ .

$\frac{v - 1 + 3 \cdot 5 (v \cdot v^{2}) - 9 v^{2}}{2 v (5 v - 3)}$

Step 5.5.1.2

Multiply $v$ by $v^{2}$ .

Tap for more steps...

Step 5.5.1.2.1

Raise $v$ to the power of $1$ .

$\frac{v - 1 + 3 \cdot 5 (v^{1} v^{2}) - 9 v^{2}}{2 v (5 v - 3)}$

Step 5.5.1.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{v - 1 + 3 \cdot 5 v^{1 + 2} - 9 v^{2}}{2 v (5 v - 3)}$

Step 5.5.1.3

Add $1$ and $2$ .

$\frac{v - 1 + 3 \cdot 5 v^{3} - 9 v^{2}}{2 v (5 v - 3)}$

Step 5.5.2

Multiply $3$ by $5$ .

$\frac{v - 1 + 15 v^{3} - 9 v^{2}}{2 v (5 v - 3)}$

Step 5.6

Reorder terms.

$\frac{15 v^{3} - 9 v^{2} + v - 1}{2 v (5 v - 3)}$