Trigonometry Examples

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

Step 1

Cancel the common factors.

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Step 1.1

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

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

Step 1.2

Cancel the common factor.

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

Step 1.3

Rewrite the expression.

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

Step 2

Simplify the numerator.

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Step 2.1

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

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

Step 2.2

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 $b = 1$ .

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

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Cancel the common factor of $t + 1$ .

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Step 3.1.1

Cancel the common factor.

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

Step 3.1.2

Rewrite the expression.

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

Step 3.2

Cancel the common factor of $t - 1$ .

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Step 3.2.1

Cancel the common factor.

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

Step 3.2.2

Rewrite the expression.

$1$