Simplify (x^2-4x-5)/(x^2-2x-15)*(7x)/(7x)

$\frac{x^{2} - 4 x - 5}{x^{2} - 2 x - 15} \cdot \frac{7 x}{7 x}$

Step 1

Cancel the common factor.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{x^{2} - 4 x - 5}{x^{2} - 2 x - 15} \cdot \frac{7 x}{7 x}$

Rewrite the expression.

$\frac{x^{2} - 4 x - 5}{x^{2} - 2 x - 15} \cdot \frac{x}{x}$

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{x^{2} - 4 x - 5}{x^{2} - 2 x - 15} \cdot \frac{x}{x}$

Rewrite the expression.

$\frac{x^{2} - 4 x - 5}{x^{2} - 2 x - 15} \cdot 1$

Step 2

Multiply $\frac{x^{2} - 4 x - 5}{x^{2} - 2 x - 15}$ by $1$ .

$\frac{x^{2} - 4 x - 5}{x^{2} - 2 x - 15}$

Step 3

Factor $x^{2} - 4 x - 5$ 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 $- 5$ and whose sum is $- 4$ .

$- 5, 1$

Write the factored form using these integers.

$\frac{(x - 5) (x + 1)}{x^{2} - 2 x - 15}$

Step 4

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.

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

Step 5

Cancel the common factor of $x - 5$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{x + 1}{x + 3}$

Simplify (x^2-4x-5)/(x^2-2x-15)*(7x)/(7x)

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