Ensembles finis Exemples

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

Step 1

Simplify the numerator.

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Step 1.1

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

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

Step 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 $b = 1$ .

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

Step 2

Cancel the common factor of $x + 1$ .

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Step 2.1

Cancel the common factor.

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

Step 2.2

Rewrite the expression.

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

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