Pre-Algebra Examples

$\frac{3 a^{2} + 3 b^{2}}{a + b} + \frac{6 a b}{b + a}$

Step 1

Simplify terms.

Tap for more steps...

Step 1.1

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

Tap for more steps...

Step 1.1.1

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

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

Step 1.1.2

Factor $3$ out of $3 b^{2}$ .

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

Step 1.1.3

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

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

Step 1.2

Reorder terms.

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

Step 1.3

Combine the numerators over the common denominator.

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

Step 2

Simplify the numerator.

Tap for more steps...

Step 2.1

Factor $3$ out of $3 (a^{2} + b^{2}) + 6 a b$ .

Tap for more steps...

Step 2.1.1

Factor $3$ out of $6 a b$ .

$\frac{3 (a^{2} + b^{2}) + 3 (2 a b)}{a + b}$

Step 2.1.2

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

$\frac{3 (a^{2} + b^{2} + 2 a b)}{a + b}$

Step 2.2

Factor using the perfect square rule.

Tap for more steps...

Step 2.2.1

Rearrange terms.

$\frac{3 (a^{2} + 2 a b + b^{2})}{a + b}$

Step 2.2.2

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$2 a b = 2 \cdot a \cdot b$

Step 2.2.3

Rewrite the polynomial.

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

Step 2.2.4

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = a$ and $b = b$ .

$\frac{3 {(a + b)}^{2}}{a + b}$

Step 3

Simplify terms.

Tap for more steps...

Step 3.1

Cancel the common factor of ${(a + b)}^{2}$ and $a + b$ .

Tap for more steps...

Step 3.1.1

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

$\frac{(a + b) (3 (a + b))}{a + b}$

Step 3.1.2

Cancel the common factors.

Tap for more steps...

Step 3.1.2.1

Multiply by $1$ .

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

Step 3.1.2.2

Cancel the common factor.

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

Step 3.1.2.3

Rewrite the expression.

$\frac{3 (a + b)}{1}$

Step 3.1.2.4

Divide $3 (a + b)$ by $1$ .

$3 (a + b)$

Step 3.2

Apply the distributive property.

$3 a + 3 b$