Simplify (5-2x)/(4x+12x^2)-(5-6x)/(4x+12x^2)

$\frac{5 - 2 x}{4 x + 12 x^{2}} - \frac{5 - 6 x}{4 x + 12 x^{2}}$

Combine the numerators over the common denominator.

$\frac{5 - 2 x - (5 - 6 x)}{12 x^{2} + 4 x}$

Simplify each term.

Apply the distributive property.

$\frac{5 - 2 x - 1 \cdot 5 - (- 6 x)}{12 x^{2} + 4 x}$

Multiply $- 1$ by $5$ .

$\frac{5 - 2 x - 5 - (- 6 x)}{12 x^{2} + 4 x}$

Multiply $- 6$ by $- 1$ .

$\frac{5 - 2 x - 5 + 6 x}{12 x^{2} + 4 x}$

Simplify terms.

Combine the opposite terms in $5 - 2 x - 5 + 6 x$ .

Subtract $5$ from $5$ .

$\frac{- 2 x + 0 + 6 x}{12 x^{2} + 4 x}$

Add $- 2 x$ and $0$ .

$\frac{- 2 x + 6 x}{12 x^{2} + 4 x}$

Add $- 2 x$ and $6 x$ .

$\frac{4 x}{12 x^{2} + 4 x}$

Factor $4 x$ out of $12 x^{2} + 4 x$ .

Factor $4 x$ out of $12 x^{2}$ .

$\frac{4 x}{4 x (3 x) + 4 x}$

Factor $4 x$ out of $4 x$ .

$\frac{4 x}{4 x (3 x) + 4 x (1)}$

Factor $4 x$ out of $4 x (3 x) + 4 x (1)$ .

$\frac{4 x}{4 x (3 x + 1)}$

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4 x (3 x + 1)}$

Rewrite the expression.

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

Cancel the common factor of $x$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{1}{3 x + 1}$