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

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

Simplify each term.

Factor $2$ out of $2 x + 2$ .

Factor $2$ out of $2 x$ .

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

Factor $2$ out of $2$ .

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

Factor $2$ out of $2 (x) + 2 (1)$ .

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

Factor $x^{2} - 2 x - 3$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 3$ and whose sum is $- 2$ .

$- 3, 1$

Write the factored form using these integers.

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

Cancel the common factor of $x + 1$ .

Cancel the common factor.

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

Rewrite the expression.

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

Combine the numerators over the common denominator.

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

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

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