Calculus Examples

$\frac{5 x^{2} - 6 x}{x^{2} - 2 x - 24}$

Step 1

Factor $x$ out of $5 x^{2} - 6 x$ .

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Step 1.1

Factor $x$ out of $5 x^{2}$ .

$\frac{x (5 x) - 6 x}{x^{2} - 2 x - 24}$

Step 1.2

Factor $x$ out of $- 6 x$ .

$\frac{x (5 x) + x \cdot - 6}{x^{2} - 2 x - 24}$

Step 1.3

Factor $x$ out of $x (5 x) + x \cdot - 6$ .

$\frac{x (5 x - 6)}{x^{2} - 2 x - 24}$

Step 2

Factor $x^{2} - 2 x - 24$ using the AC method.

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Step 2.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 24$ and whose sum is $- 2$ .

$- 6, 4$

Step 2.2

Write the factored form using these integers.

$\frac{x (5 x - 6)}{(x - 6) (x + 4)}$