Finite Math Examples

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

Step 1

Simplify the numerator.

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Step 1.1

Factor out the greatest common factor from each group.

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Step 1.1.1

Group the first two terms and the last two terms.

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

Step 1.1.2

Factor out the greatest common factor (GCF) from each group.

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

Step 1.2

Factor the polynomial by factoring out the greatest common factor, $x + 3$ .

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

Step 2

Simplify the denominator.

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Step 2.1

Factor out the greatest common factor from each group.

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Step 2.1.1

Group the first two terms and the last two terms.

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

Step 2.1.2

Factor out the greatest common factor (GCF) from each group.

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

Step 2.2

Factor the polynomial by factoring out the greatest common factor, $x + 3$ .

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

Step 3

Cancel the common factor of $x + 3$ .

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Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

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