Finite Math Examples

$\frac{5 s}{16 s^{2} - 4 t^{2}} - \frac{s}{4 s - 2 t}$

Step 1

Simplify the denominator.

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Step 1.1

Factor $4$ out of $16 s^{2} - 4 t^{2}$ .

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Step 1.1.1

Factor $4$ out of $16 s^{2}$ .

$\frac{5 s}{4 (4 s^{2}) - 4 t^{2}} - \frac{s}{4 s - 2 t}$

Step 1.1.2

Factor $4$ out of $- 4 t^{2}$ .

$\frac{5 s}{4 (4 s^{2}) + 4 (- t^{2})} - \frac{s}{4 s - 2 t}$

Step 1.1.3

Factor $4$ out of $4 (4 s^{2}) + 4 (- t^{2})$ .

$\frac{5 s}{4 (4 s^{2} - t^{2})} - \frac{s}{4 s - 2 t}$

Step 1.2

Rewrite $4 s^{2}$ as ${(2 s)}^{2}$ .

$\frac{5 s}{4 ({(2 s)}^{2} - t^{2})} - \frac{s}{4 s - 2 t}$

Step 1.3

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

$\frac{5 s}{4 (2 s + t) (2 s - t)} - \frac{s}{4 s - 2 t}$

Step 2

Factor $2$ out of $4 s - 2 t$ .

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Step 2.1

Factor $2$ out of $4 s$ .

$\frac{5 s}{4 (2 s + t) (2 s - t)} - \frac{s}{2 (2 s) - 2 t}$

Step 2.2

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

$\frac{5 s}{4 (2 s + t) (2 s - t)} - \frac{s}{2 (2 s) + 2 (- t)}$

Step 2.3

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

$\frac{5 s}{4 (2 s + t) (2 s - t)} - \frac{s}{2 (2 s - t)}$