Simplify (2x(x+1)^2-4(x+1))/(2(x^2-1))

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

Simplify the numerator.

Factor $2 (x + 1)$ out of $2 x {(x + 1)}^{2} - 4 (x + 1)$ .

Factor $2 (x + 1)$ out of $2 x {(x + 1)}^{2}$ .

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

Factor $2 (x + 1)$ out of $- 4 (x + 1)$ .

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

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

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

Apply the distributive property.

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

Multiply $x$ by $x$ .

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

Multiply $x$ by $1$ .

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

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

$- 1, 2$

Write the factored form using these integers.

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

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

Simplify the denominator.

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

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

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 $b = 1$ .

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

Reduce the expression by cancelling the common factors.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $x + 1$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $x - 1$ .

Cancel the common factor.

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

Divide $x + 2$ by $1$ .

$x + 2$

Simplify (2x(x+1)^2-4(x+1))/(2(x^2-1))

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