Basic Math Examples

$\frac{2 (\frac{17}{8})}{1 - {(\frac{17}{8})}^{2}}$

Step 1

Combine $2$ and $\frac{17}{8}$ .

$\frac{\frac{2 \cdot 17}{8}}{1 - {(\frac{17}{8})}^{2}}$

Step 2

Simplify the denominator.

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Step 2.1

Apply the product rule to $\frac{17}{8}$ .

$\frac{\frac{2 \cdot 17}{8}}{1 - \frac{17^{2}}{8^{2}}}$

Step 2.2

Raise $17$ to the power of $2$ .

$\frac{\frac{2 \cdot 17}{8}}{1 - \frac{289}{8^{2}}}$

Step 2.3

Raise $8$ to the power of $2$ .

$\frac{\frac{2 \cdot 17}{8}}{1 - \frac{289}{64}}$

Step 2.4

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

$\frac{\frac{2 \cdot 17}{8}}{\frac{64}{64} - \frac{289}{64}}$

Step 2.5

Combine the numerators over the common denominator.

$\frac{\frac{2 \cdot 17}{8}}{\frac{64 - 289}{64}}$

Step 2.6

Subtract $289$ from $64$ .

$\frac{\frac{2 \cdot 17}{8}}{\frac{- 225}{64}}$

Step 2.7

Move the negative in front of the fraction.

$\frac{\frac{2 \cdot 17}{8}}{- \frac{225}{64}}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Multiply $2$ by $17$ .

$\frac{\frac{34}{8}}{- \frac{225}{64}}$

Step 3.2

Cancel the common factor of $34$ and $8$ .

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Step 3.2.1

Factor $2$ out of $34$ .

$\frac{\frac{2 (17)}{8}}{- \frac{225}{64}}$

Step 3.2.2

Cancel the common factors.

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Step 3.2.2.1

Factor $2$ out of $8$ .

$\frac{\frac{2 \cdot 17}{2 \cdot 4}}{- \frac{225}{64}}$

Step 3.2.2.2

Cancel the common factor.

$\frac{\frac{2 \cdot 17}{2 \cdot 4}}{- \frac{225}{64}}$

Step 3.2.2.3

Rewrite the expression.

$\frac{\frac{17}{4}}{- \frac{225}{64}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\frac{17}{4} (- \frac{64}{225})$

Step 5

Cancel the common factor of $4$ .

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Step 5.1

Move the leading negative in $- \frac{64}{225}$ into the numerator.

$\frac{17}{4} \cdot \frac{- 64}{225}$

Step 5.2

Factor $4$ out of $- 64$ .

$\frac{17}{4} \cdot \frac{4 (- 16)}{225}$

Step 5.3

Cancel the common factor.

$\frac{17}{4} \cdot \frac{4 \cdot - 16}{225}$

Step 5.4

Rewrite the expression.

$17 (\frac{- 16}{225})$

Step 6

Combine $17$ and $\frac{- 16}{225}$ .

$\frac{17 \cdot - 16}{225}$

Step 7

Simplify the expression.

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Step 7.1

Multiply $17$ by $- 16$ .

$\frac{- 272}{225}$

Step 7.2

Move the negative in front of the fraction.

$- \frac{272}{225}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$- \frac{272}{225}$

Decimal Form:

$- 1.20\overline{8}$

Mixed Number Form:

$- 1 \frac{47}{225}$