Basic Math Examples

$\frac{a^{2} + 13 a - 1}{3 a + 6} - \frac{a^{2} + 7 a - 13}{3 a + 6}$

Step 1

Combine the numerators over the common denominator.

$\frac{a^{2} + 13 a - 1 - (a^{2} + 7 a - 13)}{3 a + 6}$

Step 2

Simplify each term.

Tap for more steps...

Step 2.1

Apply the distributive property.

$\frac{a^{2} + 13 a - 1 - a^{2} - (7 a) - - 13}{3 a + 6}$

Step 2.2

Simplify.

Tap for more steps...

Step 2.2.1

Multiply $7$ by $- 1$ .

$\frac{a^{2} + 13 a - 1 - a^{2} - 7 a - - 13}{3 a + 6}$

Step 2.2.2

Multiply $- 1$ by $- 13$ .

$\frac{a^{2} + 13 a - 1 - a^{2} - 7 a + 13}{3 a + 6}$

Step 3

Simplify terms.

Tap for more steps...

Step 3.1

Combine the opposite terms in $a^{2} + 13 a - 1 - a^{2} - 7 a + 13$ .

Tap for more steps...

Step 3.1.1

Subtract $a^{2}$ from $a^{2}$ .

$\frac{13 a - 1 + 0 - 7 a + 13}{3 a + 6}$

Step 3.1.2

Add $13 a - 1$ and $0$ .

$\frac{13 a - 1 - 7 a + 13}{3 a + 6}$

Step 3.2

Subtract $7 a$ from $13 a$ .

$\frac{6 a - 1 + 13}{3 a + 6}$

Step 3.3

Add $- 1$ and $13$ .

$\frac{6 a + 12}{3 a + 6}$

Step 3.4

Cancel the common factor of $6 a + 12$ and $3 a + 6$ .

Tap for more steps...

Step 3.4.1

Factor $3$ out of $6 a$ .

$\frac{3 (2 a) + 12}{3 a + 6}$

Step 3.4.2

Factor $3$ out of $12$ .

$\frac{3 (2 a) + 3 \cdot 4}{3 a + 6}$

Step 3.4.3

Factor $3$ out of $3 (2 a) + 3 (4)$ .

$\frac{3 (2 a + 4)}{3 a + 6}$

Step 3.4.4

Cancel the common factors.

Tap for more steps...

Step 3.4.4.1

Factor $3$ out of $3 a$ .

$\frac{3 (2 a + 4)}{3 (a) + 6}$

Step 3.4.4.2

Factor $3$ out of $6$ .

$\frac{3 (2 a + 4)}{3 a + 3 \cdot 2}$

Step 3.4.4.3

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

$\frac{3 (2 a + 4)}{3 (a + 2)}$

Step 3.4.4.4

Cancel the common factor.

$\frac{3 (2 a + 4)}{3 (a + 2)}$

Step 3.4.4.5

Rewrite the expression.

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

Step 3.5

Factor $2$ out of $2 a + 4$ .

Tap for more steps...

Step 3.5.1

Factor $2$ out of $2 a$ .

$\frac{2 (a) + 4}{a + 2}$

Step 3.5.2

Factor $2$ out of $4$ .

$\frac{2 a + 2 \cdot 2}{a + 2}$

Step 3.5.3

Factor $2$ out of $2 a + 2 \cdot 2$ .

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

Step 3.6

Cancel the common factor of $a + 2$ .

Tap for more steps...

Step 3.6.1

Cancel the common factor.

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

Step 3.6.2

Divide $2$ by $1$ .

$2$