Basic Math Examples

$\frac{2 t - 2}{1 - t^{2}}$

Step 1

Factor $2$ out of $2 t - 2$ .

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Step 1.1

Factor $2$ out of $2 t$ .

$\frac{2 (t) - 2}{1 - t^{2}}$

Step 1.2

Factor $2$ out of $- 2$ .

$\frac{2 (t) + 2 (- 1)}{1 - t^{2}}$

Step 1.3

Factor $2$ out of $2 (t) + 2 (- 1)$ .

$\frac{2 (t - 1)}{1 - t^{2}}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $1$ as $1^{2}$ .

$\frac{2 (t - 1)}{1^{2} - t^{2}}$

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 $a = 1$ and $b = t$ .

$\frac{2 (t - 1)}{(1 + t) (1 - t)}$

Step 3

Cancel the common factor of $t - 1$ and $1 - t$ .

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Step 3.1

Factor $- 1$ out of $t$ .

$\frac{2 (- 1 (- t) - 1)}{(1 + t) (1 - t)}$

Step 3.2

Rewrite $- 1$ as $- 1 (1)$ .

$\frac{2 (- 1 (- t) - 1 (1))}{(1 + t) (1 - t)}$

Step 3.3

Factor $- 1$ out of $- 1 (- t) - 1 (1)$ .

$\frac{2 (- 1 (- t + 1))}{(1 + t) (1 - t)}$

Step 3.4

Reorder terms.

$\frac{2 (- 1 (- t + 1))}{(1 + t) (- t + 1)}$

Step 3.5

Cancel the common factor.

$\frac{2 (- 1 (- t + 1))}{(1 + t) (- t + 1)}$

Step 3.6

Rewrite the expression.

$\frac{2 \cdot (- 1)}{1 + t}$

Step 4

Multiply $2$ by $- 1$ .

$\frac{- 2}{1 + t}$

Step 5

Move the negative in front of the fraction.

$- \frac{2}{1 + t}$