Simplify (x^2-x-6)/(5x+5)*5/(x-3)

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

Step 1

Factor $x^{2} - x - 6$ 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 $- 6$ and whose sum is $- 1$ .

$- 3, 2$

Write the factored form using these integers.

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

Step 2

Simplify terms.

Factor $5$ out of $5 x + 5$ .

Factor $5$ out of $5 x$ .

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

Factor $5$ out of $5$ .

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

Factor $5$ out of $5 (x) + 5 (1)$ .

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

Cancel the common factor of $x - 3$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{x + 2}{5 (x + 1)} \cdot 5$

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{x + 2}{5 (x + 1)} \cdot 5$

Rewrite the expression.

$\frac{x + 2}{x + 1}$

Simplify (x^2-x-6)/(5x+5)*5/(x-3)

Related Questions

Support LCMGCF.com by disabling your adblocker.