Simplify (14x-25)/(x+6)-(29-50x)/(x+6)

$\frac{14 x - 25}{x + 6} - \frac{29 - 50 x}{x + 6}$

Combine the numerators over the common denominator.

$\frac{14 x - 25 - (29 - 50 x)}{x + 6}$

Simplify each term.

Apply the distributive property.

$\frac{14 x - 25 - 1 \cdot 29 - (- 50 x)}{x + 6}$

Multiply $- 1$ by $29$ .

$\frac{14 x - 25 - 29 - (- 50 x)}{x + 6}$

Multiply $- 50$ by $- 1$ .

$\frac{14 x - 25 - 29 + 50 x}{x + 6}$

Simplify terms.

Add $14 x$ and $50 x$ .

$\frac{64 x - 25 - 29}{x + 6}$

Subtract $29$ from $- 25$ .

$\frac{64 x - 54}{x + 6}$

Factor $2$ out of $64 x - 54$ .

Factor $2$ out of $64 x$ .

$\frac{2 (32 x) - 54}{x + 6}$

Factor $2$ out of $- 54$ .

$\frac{2 (32 x) + 2 (- 27)}{x + 6}$

Factor $2$ out of $2 (32 x) + 2 (- 27)$ .

$\frac{2 (32 x - 27)}{x + 6}$