Basic Math Examples

$\frac{- 2 a + a}{2 a^{2} + 4 a - a} + 2$

Step 1

Add $- 2 a$ and $a$ .

$\frac{- a}{2 a^{2} + 4 a - a} + 2$

Step 2

Simplify each term.

Tap for more steps...

Step 2.1

Simplify the denominator.

Tap for more steps...

Step 2.1.1

Subtract $a$ from $4 a$ .

$\frac{- a}{2 a^{2} + 3 a} + 2$

Step 2.1.2

Factor $a$ out of $2 a^{2} + 3 a$ .

Tap for more steps...

Step 2.1.2.1

Factor $a$ out of $2 a^{2}$ .

$\frac{- a}{a (2 a) + 3 a} + 2$

Step 2.1.2.2

Factor $a$ out of $3 a$ .

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

Step 2.1.2.3

Factor $a$ out of $a (2 a) + a \cdot 3$ .

$\frac{- a}{a (2 a + 3)} + 2$

Step 2.2

Cancel the common factor of $a$ .

Tap for more steps...

Step 2.2.1

Cancel the common factor.

$\frac{- a}{a (2 a + 3)} + 2$

Step 2.2.2

Rewrite the expression.

$\frac{- 1}{2 a + 3} + 2$

Step 2.3

Move the negative in front of the fraction.

$- \frac{1}{2 a + 3} + 2$

Step 3

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

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Simplify the numerator.

Tap for more steps...

Step 5.1

Apply the distributive property.

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

Step 5.2

Multiply $2$ by $2$ .

$\frac{- 1 + 4 a + 2 \cdot 3}{2 a + 3}$

Step 5.3

Multiply $2$ by $3$ .

$\frac{- 1 + 4 a + 6}{2 a + 3}$

Step 5.4

Add $- 1$ and $6$ .

$\frac{4 a + 5}{2 a + 3}$