Calculus Examples

$- \frac{- 6 π}{4800 - 3 π^{2}}$

Step 1

Cancel the common factor of $- 6$ and $4800 - 3 π^{2}$ .

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Step 1.1

Factor $3$ out of $- 6 π$ .

$- \frac{3 (- 2 π)}{4800 - 3 π^{2}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $3$ out of $4800$ .

$- \frac{3 (- 2 π)}{3 (1600) - 3 π^{2}}$

Step 1.2.2

Factor $3$ out of $- 3 π^{2}$ .

$- \frac{3 (- 2 π)}{3 (1600) + 3 (- π^{2})}$

Step 1.2.3

Factor $3$ out of $3 (1600) + 3 (- π^{2})$ .

$- \frac{3 (- 2 π)}{3 (1600 - π^{2})}$

Step 1.2.4

Cancel the common factor.

$- \frac{3 (- 2 π)}{3 (1600 - π^{2})}$

Step 1.2.5

Rewrite the expression.

$- \frac{- 2 π}{1600 - π^{2}}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $1600$ as $40^{2}$ .

$- \frac{- 2 π}{40^{2} - π^{2}}$

Step 2.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 40$ and $b = π$ .

$- \frac{- 2 π}{(40 + π) (40 - π)}$

Step 3

Move the negative in front of the fraction.

$- - \frac{2 π}{(40 + π) (40 - π)}$

Step 4

Multiply $- - \frac{2 π}{(40 + π) (40 - π)}$ .

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Step 4.1

Multiply $- 1$ by $- 1$ .

$1 \frac{2 π}{(40 + π) (40 - π)}$

Step 4.2

Multiply $\frac{2 π}{(40 + π) (40 - π)}$ by $1$ .

$\frac{2 π}{(40 + π) (40 - π)}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{2 π}{(40 + π) (40 - π)}$

Decimal Form:

$0.00395136 \dots$