Simplify 11/(3(x-5))-(x+1)/(3x)

$\frac{11}{3 (x - 5)} - \frac{x + 1}{3 x}$

To write $\frac{11}{3 (x - 5)}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{11}{3 (x - 5)} \cdot \frac{x}{x} - \frac{x + 1}{3 x}$

To write $- \frac{x + 1}{3 x}$ as a fraction with a common denominator, multiply by $\frac{x - 5}{x - 5}$ .

$\frac{11}{3 (x - 5)} \cdot \frac{x}{x} - \frac{x + 1}{3 x} \cdot \frac{x - 5}{x - 5}$

Write each expression with a common denominator of $3 (x - 5) x$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{11}{3 (x - 5)}$ by $\frac{x}{x}$ .

$\frac{11 x}{3 (x - 5) x} - \frac{x + 1}{3 x} \cdot \frac{x - 5}{x - 5}$

Multiply $\frac{x + 1}{3 x}$ by $\frac{x - 5}{x - 5}$ .

$\frac{11 x}{3 (x - 5) x} - \frac{(x + 1) (x - 5)}{3 x (x - 5)}$

Reorder the factors of $3 (x - 5) x$ .

$\frac{11 x}{3 x (x - 5)} - \frac{(x + 1) (x - 5)}{3 x (x - 5)}$

Combine the numerators over the common denominator.

$\frac{11 x - (x + 1) (x - 5)}{3 x (x - 5)}$

Simplify the numerator.

Apply the distributive property.

$\frac{11 x + (- x - 1 \cdot 1) (x - 5)}{3 x (x - 5)}$

Multiply $- 1$ by $1$ .

$\frac{11 x + (- x - 1) (x - 5)}{3 x (x - 5)}$

Expand $(- x - 1) (x - 5)$ using the FOIL Method.

Apply the distributive property.

$\frac{11 x - x (x - 5) - 1 (x - 5)}{3 x (x - 5)}$

Apply the distributive property.

$\frac{11 x - x \cdot x - x \cdot - 5 - 1 (x - 5)}{3 x (x - 5)}$

Apply the distributive property.

$\frac{11 x - x \cdot x - x \cdot - 5 - 1 x - 1 \cdot - 5}{3 x (x - 5)}$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$\frac{11 x - (x \cdot x) - x \cdot - 5 - 1 x - 1 \cdot - 5}{3 x (x - 5)}$

Multiply $x$ by $x$ .

$\frac{11 x - x^{2} - x \cdot - 5 - 1 x - 1 \cdot - 5}{3 x (x - 5)}$

Multiply $- 5$ by $- 1$ .

$\frac{11 x - x^{2} + 5 x - 1 x - 1 \cdot - 5}{3 x (x - 5)}$

Rewrite $- 1 x$ as $- x$ .

$\frac{11 x - x^{2} + 5 x - x - 1 \cdot - 5}{3 x (x - 5)}$

Multiply $- 1$ by $- 5$ .

$\frac{11 x - x^{2} + 5 x - x + 5}{3 x (x - 5)}$

Subtract $x$ from $5 x$ .

$\frac{11 x - x^{2} + 4 x + 5}{3 x (x - 5)}$

Add $11 x$ and $4 x$ .

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

Simplify with factoring out.

Factor $- 1$ out of $- x^{2}$ .

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

Factor $- 1$ out of $15 x$ .

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

Factor $- 1$ out of $- (x^{2}) - (- 15 x)$ .

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

Rewrite $5$ as $- 1 (- 5)$ .

$\frac{- (x^{2} - 15 x) - 1 (- 5)}{3 x (x - 5)}$

Factor $- 1$ out of $- (x^{2} - 15 x) - 1 (- 5)$ .

$\frac{- (x^{2} - 15 x - 5)}{3 x (x - 5)}$

Simplify the expression.

Rewrite $- (x^{2} - 15 x - 5)$ as $- 1 (x^{2} - 15 x - 5)$ .

$\frac{- 1 (x^{2} - 15 x - 5)}{3 x (x - 5)}$

Move the negative in front of the fraction.

$- \frac{x^{2} - 15 x - 5}{3 x (x - 5)}$

Simplify 11/(3(x-5))-(x+1)/(3x)

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