Simplify (4x)/(x+1)*(x^2-6x-7)/(x^2-7x)

$\frac{4 x}{x + 1} \cdot \frac{x^{2} - 6 x - 7}{x^{2} - 7 x}$

Step 1

Factor $x^{2} - 6 x - 7$ 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 $- 7$ and whose sum is $- 6$ .

$- 7, 1$

Write the factored form using these integers.

$\frac{4 x}{x + 1} \cdot \frac{(x - 7) (x + 1)}{x^{2} - 7 x}$

Step 2

Simplify terms.

Factor $x$ out of $x^{2} - 7 x$ .

Factor $x$ out of $x^{2}$ .

$\frac{4 x}{x + 1} \cdot \frac{(x - 7) (x + 1)}{x \cdot x - 7 x}$

Factor $x$ out of $- 7 x$ .

$\frac{4 x}{x + 1} \cdot \frac{(x - 7) (x + 1)}{x \cdot x + x \cdot - 7}$

Factor $x$ out of $x \cdot x + x \cdot - 7$ .

$\frac{4 x}{x + 1} \cdot \frac{(x - 7) (x + 1)}{x (x - 7)}$

Cancel the common factor of $x$ .

Factor $x$ out of $4 x$ .

$\frac{x \cdot 4}{x + 1} \cdot \frac{(x - 7) (x + 1)}{x (x - 7)}$

Cancel the common factor.

$\frac{x \cdot 4}{x + 1} \cdot \frac{(x - 7) (x + 1)}{x (x - 7)}$

Rewrite the expression.

$\frac{4}{x + 1} \cdot \frac{(x - 7) (x + 1)}{x - 7}$

Cancel the common factor of $x + 1$ .

Factor $x + 1$ out of $(x - 7) (x + 1)$ .

$\frac{4}{x + 1} \cdot \frac{(x + 1) (x - 7)}{x - 7}$

Cancel the common factor.

$\frac{4}{x + 1} \cdot \frac{(x + 1) (x - 7)}{x - 7}$

Rewrite the expression.

$4 \cdot \frac{x - 7}{x - 7}$

Combine $4$ and $\frac{x - 7}{x - 7}$ .

$\frac{4 (x - 7)}{x - 7}$

Cancel the common factor of $x - 7$ .

Cancel the common factor.

$\frac{4 (x - 7)}{x - 7}$

Divide $4$ by $1$ .

$4$

Simplify (4x)/(x+1)*(x^2-6x-7)/(x^2-7x)

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