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

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

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

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

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

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

Write each expression with a common denominator of $(x - 2) (x + 3)$ , by multiplying each by an appropriate factor of $1$ .

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

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

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

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

Reorder the factors of $(x - 2) (x + 3)$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Apply the distributive property.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $3$ by $2$ .

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

Apply the distributive property.

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

Multiply $- 1$ by $5$ .

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

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $- 2$ by $- 1$ .

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

Multiply $- 5$ by $- 2$ .

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

Subtract $5 x$ from $2 x$ .

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

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

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

Subtract $3 x$ from $6 x$ .

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

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

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