Simplify (2x-10)/(x^2-2x-15)

$\frac{2 x - 10}{x^{2} - 2 x - 15}$

Step 1

Factor $2$ out of $2 x - 10$ .

Factor $2$ out of $2 x$ .

$\frac{2 (x) - 10}{x^{2} - 2 x - 15}$

Factor $2$ out of $- 10$ .

$\frac{2 x + 2 \cdot - 5}{x^{2} - 2 x - 15}$

Factor $2$ out of $2 x + 2 \cdot - 5$ .

$\frac{2 (x - 5)}{x^{2} - 2 x - 15}$

Step 2

Factor $x^{2} - 2 x - 15$ 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 $- 15$ and whose sum is $- 2$ .

$- 5, 3$

Write the factored form using these integers.

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

Step 3

Cancel the common factor of $x - 5$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify (2x-10)/(x^2-2x-15)

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