Simplify 2-(x+1)/(x-2)-(x-4)/(x+2)

$2 - \frac{x + 1}{x - 2} - \frac{x - 4}{x + 2}$

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

$\frac{2 (x - 2)}{x - 2} - \frac{x + 1}{x - 2} - \frac{x - 4}{x + 2}$

Combine the numerators over the common denominator.

$\frac{2 (x - 2) - (x + 1)}{x - 2} - \frac{x - 4}{x + 2}$

Simplify the numerator.

Apply the distributive property.

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

Multiply $2$ by $- 2$ .

$\frac{2 x - 4 - (x + 1)}{x - 2} - \frac{x - 4}{x + 2}$

Apply the distributive property.

$\frac{2 x - 4 - x - 1 \cdot 1}{x - 2} - \frac{x - 4}{x + 2}$

Multiply $- 1$ by $1$ .

$\frac{2 x - 4 - x - 1}{x - 2} - \frac{x - 4}{x + 2}$

Subtract $x$ from $2 x$ .

$\frac{x - 4 - 1}{x - 2} - \frac{x - 4}{x + 2}$

Subtract $1$ from $- 4$ .

$\frac{x - 5}{x - 2} - \frac{x - 4}{x + 2}$

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

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

To write $- \frac{x - 4}{x + 2}$ as a fraction with a common denominator, multiply by $\frac{x - 2}{x - 2}$ .

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

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

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

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

Multiply $\frac{x - 4}{x + 2}$ by $\frac{x - 2}{x - 2}$ .

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Expand $(x - 5) (x + 2)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

Move $2$ to the left of $x$ .

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

Multiply $- 5$ by $2$ .

$\frac{x^{2} + 2 x - 5 x - 10 - (x - 4) (x - 2)}{(x + 2) (x - 2)}$

Subtract $5 x$ from $2 x$ .

$\frac{x^{2} - 3 x - 10 - (x - 4) (x - 2)}{(x + 2) (x - 2)}$

Apply the distributive property.

$\frac{x^{2} - 3 x - 10 + (- x - - 4) (x - 2)}{(x + 2) (x - 2)}$

Multiply $- 1$ by $- 4$ .

$\frac{x^{2} - 3 x - 10 + (- x + 4) (x - 2)}{(x + 2) (x - 2)}$

Expand $(- x + 4) (x - 2)$ using the FOIL Method.

Apply the distributive property.

$\frac{x^{2} - 3 x - 10 - x (x - 2) + 4 (x - 2)}{(x + 2) (x - 2)}$

Apply the distributive property.

$\frac{x^{2} - 3 x - 10 - x \cdot x - x \cdot - 2 + 4 (x - 2)}{(x + 2) (x - 2)}$

Apply the distributive property.

$\frac{x^{2} - 3 x - 10 - x \cdot x - x \cdot - 2 + 4 x + 4 \cdot - 2}{(x + 2) (x - 2)}$

Simplify and combine like terms.

Simplify each term.

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

Move $x$ .

$\frac{x^{2} - 3 x - 10 - (x \cdot x) - x \cdot - 2 + 4 x + 4 \cdot - 2}{(x + 2) (x - 2)}$

Multiply $x$ by $x$ .

$\frac{x^{2} - 3 x - 10 - x^{2} - x \cdot - 2 + 4 x + 4 \cdot - 2}{(x + 2) (x - 2)}$

Multiply $- 2$ by $- 1$ .

$\frac{x^{2} - 3 x - 10 - x^{2} + 2 x + 4 x + 4 \cdot - 2}{(x + 2) (x - 2)}$

Multiply $4$ by $- 2$ .

$\frac{x^{2} - 3 x - 10 - x^{2} + 2 x + 4 x - 8}{(x + 2) (x - 2)}$

Add $2 x$ and $4 x$ .

$\frac{x^{2} - 3 x - 10 - x^{2} + 6 x - 8}{(x + 2) (x - 2)}$

Subtract $x^{2}$ from $x^{2}$ .

$\frac{- 3 x - 10 + 0 + 6 x - 8}{(x + 2) (x - 2)}$

Add $- 3 x$ and $0$ .

$\frac{- 3 x - 10 + 6 x - 8}{(x + 2) (x - 2)}$

Add $- 3 x$ and $6 x$ .

$\frac{3 x - 10 - 8}{(x + 2) (x - 2)}$

Subtract $8$ from $- 10$ .

$\frac{3 x - 18}{(x + 2) (x - 2)}$

Factor $3$ out of $3 x - 18$ .

Factor $3$ out of $3 x$ .

$\frac{3 (x) - 18}{(x + 2) (x - 2)}$

Factor $3$ out of $- 18$ .

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

Factor $3$ out of $3 x + 3 \cdot - 6$ .

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

Simplify 2-(x+1)/(x-2)-(x-4)/(x+2)

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