Finite Math Examples

$\frac{x^{2} - 10 x + 25}{x^{3} - 12^{2} + 50 x}$

Step 1

Factor using the perfect square rule.

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Step 1.1

Rewrite $25$ as $5^{2}$ .

$\frac{x^{2} - 10 x + 5^{2}}{x^{3} - 12^{2} + 50 x}$

Step 1.2

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$10 x = 2 \cdot x \cdot 5$

Step 1.3

Rewrite the polynomial.

$\frac{x^{2} - 2 \cdot x \cdot 5 + 5^{2}}{x^{3} - 12^{2} + 50 x}$

Step 1.4

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = x$ and $b = 5$ .

$\frac{{(x - 5)}^{2}}{x^{3} - 12^{2} + 50 x}$

Step 2

Simplify the denominator.

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Step 2.1

Raise $12$ to the power of $2$ .

$\frac{{(x - 5)}^{2}}{x^{3} - 1 \cdot 144 + 50 x}$

Step 2.2

Multiply $- 1$ by $144$ .

$\frac{{(x - 5)}^{2}}{x^{3} - 144 + 50 x}$

Step 2.3

Reorder terms.

$\frac{{(x - 5)}^{2}}{x^{3} + 50 x - 144}$