Algebra Examples

$\frac{4 t - 8}{4 - t^{2}}$

Step 1

Factor $4$ out of $4 t - 8$ .

Tap for more steps...

Factor $4$ out of $4 t$ .

$\frac{4 (t) - 8}{4 - t^{2}}$

Factor $4$ out of $- 8$ .

$\frac{4 t + 4 \cdot - 2}{4 - t^{2}}$

Factor $4$ out of $4 t + 4 \cdot - 2$ .

$\frac{4 (t - 2)}{4 - t^{2}}$

Step 2

Simplify the denominator.

Tap for more steps...

Rewrite $4$ as $2^{2}$ .

$\frac{4 (t - 2)}{2^{2} - t^{2}}$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 2$ and $b = t$ .

$\frac{4 (t - 2)}{(2 + t) (2 - t)}$

Step 3

Cancel the common factor of $t - 2$ and $2 - t$ .

Tap for more steps...

Factor $- 1$ out of $t$ .

$\frac{4 (- 1 (- t) - 2)}{(2 + t) (2 - t)}$

Rewrite $- 2$ as $- 1 (2)$ .

$\frac{4 (- 1 (- t) - 1 (2))}{(2 + t) (2 - t)}$

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

$\frac{4 (- 1 (- t + 2))}{(2 + t) (2 - t)}$

Reorder terms.

$\frac{4 (- 1 (- t + 2))}{(2 + t) (- t + 2)}$

Cancel the common factor.

$\frac{4 (- 1 (- t + 2))}{(2 + t) (- t + 2)}$

Rewrite the expression.

$\frac{4 \cdot (- 1)}{2 + t}$

Step 4

Multiply $4$ by $- 1$ .

$\frac{- 4}{2 + t}$

Step 5

Move the negative in front of the fraction.

$- \frac{4}{2 + t}$