Simplify ((t+1)(t^2-1))/((t-1)(t+1)^2)

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Trigonometry

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the numerator.

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

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

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

$\frac{(t + 1) (t - 1)}{(t - 1) (t + 1)}$

Reduce the expression by cancelling the common factors.

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Cancel the common factor of $t + 1$ .

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Cancel the common factor.

$\frac{(t + 1) (t - 1)}{(t - 1) (t + 1)}$

Rewrite the expression.

$\frac{t - 1}{t - 1}$

Cancel the common factor of $t - 1$ .

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Cancel the common factor.

$\frac{t - 1}{t - 1}$

Divide $1$ by $1$ .

$1$

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