Evaluate (2(-12/5))/(1-(-12/5)^2)

$\frac{2 (- \frac{12}{5})}{1 - {(- \frac{12}{5})}^{2}}$

Simplify the numerator.

Multiply $- 1$ by $2$ .

$\frac{- 2 (\frac{12}{5})}{1 - {(- \frac{12}{5})}^{2}}$

Combine $- 2$ and $\frac{12}{5}$ .

$\frac{\frac{- 2 \cdot 12}{5}}{1 - {(- \frac{12}{5})}^{2}}$

Simplify the denominator.

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $- \frac{12}{5}$ .

$\frac{\frac{- 2 \cdot 12}{5}}{1 - ({(- 1)}^{2} {(\frac{12}{5})}^{2})}$

Apply the product rule to $\frac{12}{5}$ .

$\frac{\frac{- 2 \cdot 12}{5}}{1 - ({(- 1)}^{2} \frac{12^{2}}{5^{2}})}$

Multiply $- 1$ by ${(- 1)}^{2}$ by adding the exponents.

Move ${(- 1)}^{2}$ .

$\frac{\frac{- 2 \cdot 12}{5}}{1 + {(- 1)}^{2} \cdot - 1 \frac{12^{2}}{5^{2}}}$

Multiply ${(- 1)}^{2}$ by $- 1$ .

Raise $- 1$ to the power of $1$ .

$\frac{\frac{- 2 \cdot 12}{5}}{1 + {(- 1)}^{2} \cdot {(- 1)}^{1} \frac{12^{2}}{5^{2}}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{\frac{- 2 \cdot 12}{5}}{1 + {(- 1)}^{2 + 1} \frac{12^{2}}{5^{2}}}$

Add $2$ and $1$ .

$\frac{\frac{- 2 \cdot 12}{5}}{1 + {(- 1)}^{3} \frac{12^{2}}{5^{2}}}$

Raise $- 1$ to the power of $3$ .

$\frac{\frac{- 2 \cdot 12}{5}}{1 - \frac{12^{2}}{5^{2}}}$

Raise $12$ to the power of $2$ .

$\frac{\frac{- 2 \cdot 12}{5}}{1 - \frac{144}{5^{2}}}$

Raise $5$ to the power of $2$ .

$\frac{\frac{- 2 \cdot 12}{5}}{1 - \frac{144}{25}}$

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

$\frac{\frac{- 2 \cdot 12}{5}}{\frac{25}{25} - \frac{144}{25}}$

Combine the numerators over the common denominator.

$\frac{\frac{- 2 \cdot 12}{5}}{\frac{25 - 144}{25}}$

Subtract $144$ from $25$ .

$\frac{\frac{- 2 \cdot 12}{5}}{\frac{- 119}{25}}$

Move the negative in front of the fraction.

$\frac{\frac{- 2 \cdot 12}{5}}{- \frac{119}{25}}$

Reduce the expression by cancelling the common factors.

Multiply $- 2$ by $12$ .

$\frac{\frac{- 24}{5}}{- \frac{119}{25}}$

Move the negative in front of the fraction.

$\frac{- \frac{24}{5}}{- \frac{119}{25}}$

Dividing two negative values results in a positive value.

$\frac{\frac{24}{5}}{\frac{119}{25}}$

Multiply the numerator by the reciprocal of the denominator.

$\frac{24}{5} \cdot \frac{25}{119}$

Cancel the common factor of $5$ .

Factor $5$ out of $25$ .

$\frac{24}{5} \cdot \frac{5 (5)}{119}$

Cancel the common factor.

$\frac{24}{5} \cdot \frac{5 \cdot 5}{119}$

Rewrite the expression.

$24 (\frac{5}{119})$

Combine $24$ and $\frac{5}{119}$ .

$\frac{24 \cdot 5}{119}$

Multiply $24$ by $5$ .

$\frac{120}{119}$

The result can be shown in multiple forms.

Exact Form:

$\frac{120}{119}$

Decimal Form:

$1.00840336 \dots$

Mixed Number Form:

$1 \frac{1}{119}$

Evaluate (2(-12/5))/(1-(-12/5)^2)

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