Finite Math Examples

$2.1 x^{3} - x^{1 + \frac{x^{2} - 3}{2}}$

Step 1

Write $1$ as a fraction with a common denominator.

$2.1 x^{3} - x^{\frac{2}{2} + \frac{x^{2} - 3}{2}}$

Step 2

Combine the numerators over the common denominator.

$2.1 x^{3} - x^{\frac{2 + x^{2} - 3}{2}}$

Step 3

Simplify the numerator.

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Step 3.1

Subtract $3$ from $2$ .

$2.1 x^{3} - x^{\frac{x^{2} - 1}{2}}$

Step 3.2

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

$2.1 x^{3} - x^{\frac{x^{2} - 1^{2}}{2}}$

Step 3.3

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 $b = 1$ .

$2.1 x^{3} - x^{\frac{(x + 1) (x - 1)}{2}}$