Basic Math Examples

$\frac{t^{2} - 4}{t^{2} - 11 + 24} \cdot \frac{5 t - 2}{5 t + 2}$

Step 1

Simplify the numerator.

Tap for more steps...

Step 1.1

Rewrite

$4$ as

$2^{2}$ .

$\frac{t^{2} - 2^{2}}{t^{2} - 11 + 24} \cdot \frac{5 t - 2}{5 t + 2}$

Step 1.2

Since both terms are perfect squares, factor using the difference of squares formula,

$a^{2} - b^{2} = (a + b) (a - b)$ where

$a = t$ and

$b = 2$ .

$\frac{(t + 2) (t - 2)}{t^{2} - 11 + 24} \cdot \frac{5 t - 2}{5 t + 2}$

Step 2

Combine fractions.

Tap for more steps...

Step 2.1

Add

$- 11$ and

$24$ .

$\frac{(t + 2) (t - 2)}{t^{2} + 13} \cdot \frac{5 t - 2}{5 t + 2}$

Step 2.2

Multiply

$\frac{(t + 2) (t - 2)}{t^{2} + 13}$ by

$\frac{5 t - 2}{5 t + 2}$ .

$\frac{(t + 2) (t - 2) (5 t - 2)}{(t^{2} + 13) (5 t + 2)}$