Simplify (x-3)/(x+2)-(x+4)/(x-2)

$\frac{x - 3}{x + 2} - \frac{x + 4}{x - 2}$

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

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

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

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

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

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

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

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Expand $(x - 3) (x - 2)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

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

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

Multiply $- 3$ by $- 2$ .

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

Subtract $3 x$ from $- 2 x$ .

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

Apply the distributive property.

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

Multiply $- 1$ by $4$ .

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

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $2$ by $- 1$ .

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

Multiply $- 4$ by $2$ .

$\frac{x^{2} - 5 x + 6 - x^{2} - 2 x - 4 x - 8}{(x + 2) (x - 2)}$

Subtract $4 x$ from $- 2 x$ .

$\frac{x^{2} - 5 x + 6 - x^{2} - 6 x - 8}{(x + 2) (x - 2)}$

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

$\frac{- 5 x + 6 + 0 - 6 x - 8}{(x + 2) (x - 2)}$

Add $- 5 x$ and $0$ .

$\frac{- 5 x + 6 - 6 x - 8}{(x + 2) (x - 2)}$

Subtract $6 x$ from $- 5 x$ .

$\frac{- 11 x + 6 - 8}{(x + 2) (x - 2)}$

Subtract $8$ from $6$ .

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

Simplify with factoring out.

Factor $- 1$ out of $- 11 x$ .

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

Rewrite $- 2$ as $- 1 (2)$ .

$\frac{- (11 x) - 1 (2)}{(x + 2) (x - 2)}$

Factor $- 1$ out of $- (11 x) - 1 (2)$ .

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

Simplify the expression.

Rewrite $- (11 x + 2)$ as $- 1 (11 x + 2)$ .

$\frac{- 1 (11 x + 2)}{(x + 2) (x - 2)}$

Move the negative in front of the fraction.

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

Simplify (x-3)/(x+2)-(x+4)/(x-2)

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