Calculus Examples

$\frac{5 x^{3} + 8 x^{2}}{3 x^{4} - 16 x^{2}}$

Step 1

Factor $x^{2}$ out of $5 x^{3} + 8 x^{2}$ .

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Step 1.1

Factor $x^{2}$ out of $5 x^{3}$ .

$\frac{x^{2} (5 x) + 8 x^{2}}{3 x^{4} - 16 x^{2}}$

Step 1.2

Factor $x^{2}$ out of $8 x^{2}$ .

$\frac{x^{2} (5 x) + x^{2} \cdot 8}{3 x^{4} - 16 x^{2}}$

Step 1.3

Factor $x^{2}$ out of $x^{2} (5 x) + x^{2} \cdot 8$ .

$\frac{x^{2} (5 x + 8)}{3 x^{4} - 16 x^{2}}$

Step 2

Factor $x^{2}$ out of $3 x^{4} - 16 x^{2}$ .

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Step 2.1

Factor $x^{2}$ out of $3 x^{4}$ .

$\frac{x^{2} (5 x + 8)}{x^{2} (3 x^{2}) - 16 x^{2}}$

Step 2.2

Factor $x^{2}$ out of $- 16 x^{2}$ .

$\frac{x^{2} (5 x + 8)}{x^{2} (3 x^{2}) + x^{2} \cdot - 16}$

Step 2.3

Factor $x^{2}$ out of $x^{2} (3 x^{2}) + x^{2} \cdot - 16$ .

$\frac{x^{2} (5 x + 8)}{x^{2} (3 x^{2} - 16)}$

Step 3

Cancel the common factor of $x^{2}$ .

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Step 3.1

Cancel the common factor.

$\frac{x^{2} (5 x + 8)}{x^{2} (3 x^{2} - 16)}$

Step 3.2

Rewrite the expression.

$\frac{5 x + 8}{3 x^{2} - 16}$