Simplify (x^2+8x)/(3x^2+3x)-(x^2+2x-6)/(3x^2+3x)

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

Combine the numerators over the common denominator.

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

Simplify each term.

Apply the distributive property.

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

Simplify.

Multiply $2$ by $- 1$ .

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

Multiply $- 1$ by $- 6$ .

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

Simplify terms.

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

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

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

Add $8 x$ and $0$ .

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

Subtract $2 x$ from $8 x$ .

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

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

Factor $6$ out of $6 x$ .

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

Factor $6$ out of $6$ .

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

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

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

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

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

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

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

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

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

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

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

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

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $x + 1$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{2}{x}$

Simplify (x^2+8x)/(3x^2+3x)-(x^2+2x-6)/(3x^2+3x)

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