Finite Math Examples

$x = \frac{50000 \cdot \frac{5}{6}}{1 - {(1 + \frac{5}{6})}^{- 90}}$

Step 1

Combine $50000$ and $\frac{5}{6}$ .

$x = \frac{\frac{50000 \cdot 5}{6}}{1 - {(1 + \frac{5}{6})}^{- 90}}$

Step 2

Simplify the denominator.

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Step 2.1

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

$x = \frac{\frac{50000 \cdot 5}{6}}{1 - {(\frac{6}{6} + \frac{5}{6})}^{- 90}}$

Step 2.2

Combine the numerators over the common denominator.

$x = \frac{\frac{50000 \cdot 5}{6}}{1 - {(\frac{6 + 5}{6})}^{- 90}}$

Step 2.3

Add $6$ and $5$ .

$x = \frac{\frac{50000 \cdot 5}{6}}{1 - {(\frac{11}{6})}^{- 90}}$

Step 2.4

Change the sign of the exponent by rewriting the base as its reciprocal.

$x = \frac{\frac{50000 \cdot 5}{6}}{1 - {(\frac{6}{11})}^{90}}$

Step 2.5

Apply the product rule to $\frac{6}{11}$ .

$x = \frac{\frac{50000 \cdot 5}{6}}{1 - \frac{6^{90}}{11^{90}}}$

Step 2.6

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

$x = \frac{\frac{50000 \cdot 5}{6}}{\frac{11^{90}}{11^{90}} - \frac{6^{90}}{11^{90}}}$

Step 2.7

Combine the numerators over the common denominator.

$x = \frac{\frac{50000 \cdot 5}{6}}{\frac{11^{90} - 6^{90}}{11^{90}}}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Multiply $50000$ by $5$ .

$x = \frac{\frac{250000}{6}}{\frac{11^{90} - 6^{90}}{11^{90}}}$

Step 3.2

Cancel the common factor of $250000$ and $6$ .

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Step 3.2.1

Factor $2$ out of $250000$ .

$x = \frac{\frac{2 (125000)}{6}}{\frac{11^{90} - 6^{90}}{11^{90}}}$

Step 3.2.2

Cancel the common factors.

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Step 3.2.2.1

Factor $2$ out of $6$ .

$x = \frac{\frac{2 \cdot 125000}{2 \cdot 3}}{\frac{11^{90} - 6^{90}}{11^{90}}}$

Step 3.2.2.2

Cancel the common factor.

$x = \frac{\frac{2 \cdot 125000}{2 \cdot 3}}{\frac{11^{90} - 6^{90}}{11^{90}}}$

Step 3.2.2.3

Rewrite the expression.

$x = \frac{\frac{125000}{3}}{\frac{11^{90} - 6^{90}}{11^{90}}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$x = \frac{125000}{3} \cdot \frac{11^{90}}{11^{90} - 6^{90}}$

Step 5

Multiply $\frac{125000}{3}$ by $\frac{11^{90}}{11^{90} - 6^{90}}$ .

$x = \frac{125000 \cdot 11^{90}}{3 (11^{90} - 6^{90})}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{125000 \cdot 11^{90}}{3 (11^{90} - 6^{90})}$

Decimal Form:

$x = 41666.\overline{6}$