Simplify (3x)/(2x+2)*(x^2-1)/(x^2+6x-7)

$\frac{3 x}{2 x + 2} \cdot \frac{x^{2} - 1}{x^{2} + 6 x - 7}$

Factor $2$ out of $2 x + 2$ .

Factor $2$ out of $2 x$ .

$\frac{3 x}{2 (x) + 2} \cdot \frac{x^{2} - 1}{x^{2} + 6 x - 7}$

Factor $2$ out of $2$ .

$\frac{3 x}{2 (x) + 2 (1)} \cdot \frac{x^{2} - 1}{x^{2} + 6 x - 7}$

Factor $2$ out of $2 (x) + 2 (1)$ .

$\frac{3 x}{2 (x + 1)} \cdot \frac{x^{2} - 1}{x^{2} + 6 x - 7}$

Simplify the numerator.

Rewrite $1$ as $1^{2}$ .

$\frac{3 x}{2 (x + 1)} \cdot \frac{x^{2} - 1^{2}}{x^{2} + 6 x - 7}$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 1$ .

$\frac{3 x}{2 (x + 1)} \cdot \frac{(x + 1) (x - 1)}{x^{2} + 6 x - 7}$

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 $6$ .

$- 1, 7$

Write the factored form using these integers.

$\frac{3 x}{2 (x + 1)} \cdot \frac{(x + 1) (x - 1)}{(x - 1) (x + 7)}$

Simplify terms.

Cancel the common factor of $x + 1$ .

Factor $x + 1$ out of $2 (x + 1)$ .

$\frac{3 x}{(x + 1) \cdot 2} \cdot \frac{(x + 1) (x - 1)}{(x - 1) (x + 7)}$

Cancel the common factor.

$\frac{3 x}{(x + 1) \cdot 2} \cdot \frac{(x + 1) (x - 1)}{(x - 1) (x + 7)}$

Rewrite the expression.

$\frac{3 x}{2} \cdot \frac{x - 1}{(x - 1) (x + 7)}$

Multiply $\frac{3 x}{2}$ by $\frac{x - 1}{(x - 1) (x + 7)}$ .

$\frac{3 x (x - 1)}{2 ((x - 1) (x + 7))}$

Cancel the common factor of $x - 1$ .

Cancel the common factor.

$\frac{3 x (x - 1)}{2 ((x - 1) (x + 7))}$

Rewrite the expression.

$\frac{3 x}{2 (x + 7)}$

Simplify (3x)/(2x+2)*(x^2-1)/(x^2+6x-7)

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