Simplify (2x+3)/(5x-30)-(3x+4)/(x-6)

$\frac{2 x + 3}{5 x - 30} - \frac{3 x + 4}{x - 6}$

Factor $5$ out of $5 x - 30$ .

Factor $5$ out of $5 x$ .

$\frac{2 x + 3}{5 (x) - 30} - \frac{3 x + 4}{x - 6}$

Factor $5$ out of $- 30$ .

$\frac{2 x + 3}{5 x + 5 \cdot - 6} - \frac{3 x + 4}{x - 6}$

Factor $5$ out of $5 x + 5 \cdot - 6$ .

$\frac{2 x + 3}{5 (x - 6)} - \frac{3 x + 4}{x - 6}$

To write $- \frac{3 x + 4}{x - 6}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{2 x + 3}{5 (x - 6)} - \frac{3 x + 4}{x - 6} \cdot \frac{5}{5}$

Write each expression with a common denominator of $5 (x - 6)$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{3 x + 4}{x - 6}$ by $\frac{5}{5}$ .

$\frac{2 x + 3}{5 (x - 6)} - \frac{(3 x + 4) \cdot 5}{(x - 6) \cdot 5}$

Reorder the factors of $(x - 6) \cdot 5$ .

$\frac{2 x + 3}{5 (x - 6)} - \frac{(3 x + 4) \cdot 5}{5 (x - 6)}$

Combine the numerators over the common denominator.

$\frac{2 x + 3 - (3 x + 4) \cdot 5}{5 (x - 6)}$

Simplify the numerator.

Apply the distributive property.

$\frac{2 x + 3 + (- (3 x) - 1 \cdot 4) \cdot 5}{5 (x - 6)}$

Multiply $3$ by $- 1$ .

$\frac{2 x + 3 + (- 3 x - 1 \cdot 4) \cdot 5}{5 (x - 6)}$

Multiply $- 1$ by $4$ .

$\frac{2 x + 3 + (- 3 x - 4) \cdot 5}{5 (x - 6)}$

Apply the distributive property.

$\frac{2 x + 3 - 3 x \cdot 5 - 4 \cdot 5}{5 (x - 6)}$

Multiply $5$ by $- 3$ .

$\frac{2 x + 3 - 15 x - 4 \cdot 5}{5 (x - 6)}$

Multiply $- 4$ by $5$ .

$\frac{2 x + 3 - 15 x - 20}{5 (x - 6)}$

Subtract $15 x$ from $2 x$ .

$\frac{- 13 x + 3 - 20}{5 (x - 6)}$

Subtract $20$ from $3$ .

$\frac{- 13 x - 17}{5 (x - 6)}$

Simplify with factoring out.

Factor $- 1$ out of $- 13 x$ .

$\frac{- (13 x) - 17}{5 (x - 6)}$

Rewrite $- 17$ as $- 1 (17)$ .

$\frac{- (13 x) - 1 (17)}{5 (x - 6)}$

Factor $- 1$ out of $- (13 x) - 1 (17)$ .

$\frac{- (13 x + 17)}{5 (x - 6)}$

Simplify the expression.

Rewrite $- (13 x + 17)$ as $- 1 (13 x + 17)$ .

$\frac{- 1 (13 x + 17)}{5 (x - 6)}$

Move the negative in front of the fraction.

$- \frac{13 x + 17}{5 (x - 6)}$

Simplify (2x+3)/(5x-30)-(3x+4)/(x-6)

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