Simplify 5-(2x+5)/(x-6)

$5 - \frac{2 x + 5}{x - 6}$

Step 1

To write $5$ as a fraction with a common denominator, multiply by $\frac{x - 6}{x - 6}$ .

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

Step 2

Combine the numerators over the common denominator.

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

Step 3

Simplify the numerator.

Apply the distributive property.

$\frac{5 x + 5 \cdot - 6 - (2 x + 5)}{x - 6}$

Multiply $5$ by $- 6$ .

$\frac{5 x - 30 - (2 x + 5)}{x - 6}$

Apply the distributive property.

$\frac{5 x - 30 - (2 x) - 1 \cdot 5}{x - 6}$

Multiply $2$ by $- 1$ .

$\frac{5 x - 30 - 2 x - 1 \cdot 5}{x - 6}$

Multiply $- 1$ by $5$ .

$\frac{5 x - 30 - 2 x - 5}{x - 6}$

Subtract $2 x$ from $5 x$ .

$\frac{3 x - 30 - 5}{x - 6}$

Subtract $5$ from $- 30$ .

$\frac{3 x - 35}{x - 6}$