Simplify ((x^2-2x-3)/(x+1))÷((x-3)/5)

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

To divide by a fraction, multiply by its reciprocal.

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

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.

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

Simplify terms.

Cancel the common factor of $x - 3$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{x + 1}{x + 1} \cdot 5$

Combine $\frac{x + 1}{x + 1}$ and $5$ .

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

Cancel the common factor of $x + 1$ .

Cancel the common factor.

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

Divide $5$ by $1$ .

$5$

Simplify ((x^2-2x-3)/(x+1))÷((x-3)/5)

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