Simplify (7w-2)/(16w^2-1)

$\frac{7 w - 2}{16 w^{2} - 1}$

Step 1

Rewrite $16 w^{2}$ as ${(4 w)}^{2}$ .

$\frac{7 w - 2}{{(4 w)}^{2} - 1}$

Step 2

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

$\frac{7 w - 2}{{(4 w)}^{2} - 1^{2}}$

Step 3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 4 w$ and $b = 1$ .

$\frac{7 w - 2}{(4 w + 1) (4 w - 1)}$