Algebra Examples

$\frac{x^{2} + 8 x}{3 x^{2} + 3 x} - \frac{x^{2} + 2 x - 6}{3 x^{2} + 3 x}$

Step 1

Combine the numerators over the common denominator.

$\frac{x^{2} + 8 x - (x^{2} + 2 x - 6)}{3 x^{2} + 3 x}$

Step 2

Simplify each term.

Tap for more steps...

Step 2.1

Apply the distributive property.

$\frac{x^{2} + 8 x - x^{2} - (2 x) - - 6}{3 x^{2} + 3 x}$

Step 2.2

Simplify.

Tap for more steps...

Step 2.2.1

Multiply $2$ by $- 1$ .

$\frac{x^{2} + 8 x - x^{2} - 2 x - - 6}{3 x^{2} + 3 x}$

Step 2.2.2

Multiply $- 1$ by $- 6$ .

$\frac{x^{2} + 8 x - x^{2} - 2 x + 6}{3 x^{2} + 3 x}$

Step 3

Simplify terms.

Tap for more steps...

Step 3.1

Combine the opposite terms in $x^{2} + 8 x - x^{2} - 2 x + 6$ .

Tap for more steps...

Step 3.1.1

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

$\frac{8 x + 0 - 2 x + 6}{3 x^{2} + 3 x}$

Step 3.1.2

Add $8 x$ and $0$ .

$\frac{8 x - 2 x + 6}{3 x^{2} + 3 x}$

Step 3.2

Subtract $2 x$ from $8 x$ .

$\frac{6 x + 6}{3 x^{2} + 3 x}$

Step 3.3

Factor $6$ out of $6 x + 6$ .

Tap for more steps...

Step 3.3.1

Factor $6$ out of $6 x$ .

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

Step 3.3.2

Factor $6$ out of $6$ .

$\frac{6 (x) + 6 (1)}{3 x^{2} + 3 x}$

Step 3.3.3

Factor $6$ out of $6 (x) + 6 (1)$ .

$\frac{6 (x + 1)}{3 x^{2} + 3 x}$

Step 3.4

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

Tap for more steps...

Step 3.4.1

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

$\frac{6 (x + 1)}{3 x (x) + 3 x}$

Step 3.4.2

Factor $3 x$ out of $3 x$ .

$\frac{6 (x + 1)}{3 x (x) + 3 x (1)}$

Step 3.4.3

Factor $3 x$ out of $3 x (x) + 3 x (1)$ .

$\frac{6 (x + 1)}{3 x (x + 1)}$

Step 3.5

Cancel the common factor of $6$ and $3$ .

Tap for more steps...

Step 3.5.1

Factor $3$ out of $6 (x + 1)$ .

$\frac{3 (2 (x + 1))}{3 x (x + 1)}$

Step 3.5.2

Cancel the common factors.

Tap for more steps...

Step 3.5.2.1

Factor $3$ out of $3 x (x + 1)$ .

$\frac{3 (2 (x + 1))}{3 (x (x + 1))}$

Step 3.5.2.2

Cancel the common factor.

$\frac{3 (2 (x + 1))}{3 (x (x + 1))}$

Step 3.5.2.3

Rewrite the expression.

$\frac{2 (x + 1)}{x (x + 1)}$

Step 3.6

Cancel the common factor of $x + 1$ .

Tap for more steps...

Step 3.6.1

Cancel the common factor.

$\frac{2 (x + 1)}{x (x + 1)}$

Step 3.6.2

Rewrite the expression.

$\frac{2}{x}$