Algebra Examples

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

Step 1

Simplify the numerator.

Tap for more steps...

Step 1.1

Multiply $- 1$ by $2$ .

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

Step 1.2

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

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

Step 2

Simplify the denominator.

Tap for more steps...

Step 2.1

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

Tap for more steps...

Step 2.1.1

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

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

Step 2.1.2

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

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

Step 2.2

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

Tap for more steps...

Step 2.2.1

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

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

Step 2.2.2

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

Tap for more steps...

Step 2.2.2.1

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

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

Step 2.2.2.2

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

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

Step 2.2.3

Add $2$ and $1$ .

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

Step 2.3

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

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

Step 2.4

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

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

Step 2.5

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

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

Step 2.6

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

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

Step 2.7

Combine the numerators over the common denominator.

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

Step 2.8

Subtract $144$ from $25$ .

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

Step 2.9

Move the negative in front of the fraction.

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

Step 3

Reduce the expression by cancelling the common factors.

Tap for more steps...

Step 3.1

Multiply $- 2$ by $12$ .

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

Step 3.2

Move the negative in front of the fraction.

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

Step 3.3

Dividing two negative values results in a positive value.

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

Step 4

Multiply the numerator by the reciprocal of the denominator.

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

Step 5

Cancel the common factor of $5$ .

Tap for more steps...

Step 5.1

Factor $5$ out of $25$ .

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

Step 5.2

Cancel the common factor.

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

Step 5.3

Rewrite the expression.

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

Step 6

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

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

Step 7

Multiply $24$ by $5$ .

$\frac{120}{119}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{120}{119}$

Decimal Form:

$1.00840336 \dots$

Mixed Number Form:

$1 \frac{1}{119}$