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

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

Multiply the numerator by the reciprocal of the denominator.

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

To write $\frac{3}{x + 5}$ as a fraction with a common denominator, multiply by $\frac{x - 2}{x - 2}$ .

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

To write $\frac{2}{x - 2}$ as a fraction with a common denominator, multiply by $\frac{x + 5}{x + 5}$ .

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

Write each expression with a common denominator of $(x + 5) (x - 2)$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{3}{x + 5}$ by $\frac{x - 2}{x - 2}$ .

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

Multiply $\frac{2}{x - 2}$ by $\frac{x + 5}{x + 5}$ .

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

Reorder the factors of $(x - 2) (x + 5)$ .

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

Simplify terms.

Combine the numerators over the common denominator.

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

Rewrite using the commutative property of multiplication.

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

Cancel the common factor of $x - 2$ .

Move the leading negative in $- \frac{3 (x - 2) + 2 (x + 5)}{(x + 5) (x - 2)}$ into the numerator.

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

Factor $x - 2$ out of $(x + 5) (x - 2)$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $\frac{- (3 (x - 2) + 2 (x + 5))}{x + 5}$ by $\frac{1}{6}$ .

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

Simplify the numerator.

Apply the distributive property.

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

Multiply $3$ by $- 2$ .

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

Apply the distributive property.

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

Multiply $2$ by $5$ .

$\frac{- (3 x - 6 + 2 x + 10)}{(x + 5) \cdot 6}$

Add $3 x$ and $2 x$ .

$\frac{- (5 x - 6 + 10)}{(x + 5) \cdot 6}$

Add $- 6$ and $10$ .

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

Simplify the expression.

Move $6$ to the left of $x + 5$ .

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

Move the negative in front of the fraction.

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

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

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