Basic Math Examples

$\frac{b^{2}}{81 b^{2} - 64} \div \frac{b}{72 b + 64}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{b^{2}}{81 b^{2} - 64} \cdot \frac{72 b + 64}{b}$

Step 2

Cancel the common factor of $b$ .

Tap for more steps...

Step 2.1

Factor $b$ out of $b^{2}$ .

$\frac{b \cdot b}{81 b^{2} - 64} \cdot \frac{72 b + 64}{b}$

Step 2.2

Cancel the common factor.

$\frac{b \cdot b}{81 b^{2} - 64} \cdot \frac{72 b + 64}{b}$

Step 2.3

Rewrite the expression.

$\frac{b}{81 b^{2} - 64} (72 b + 64)$

Step 3

Simplify the denominator.

Tap for more steps...

Step 3.1

Rewrite $81 b^{2}$ as ${(9 b)}^{2}$ .

$\frac{b}{{(9 b)}^{2} - 64} (72 b + 64)$

Step 3.2

Rewrite $64$ as $8^{2}$ .

$\frac{b}{{(9 b)}^{2} - 8^{2}} (72 b + 64)$

Step 3.3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 9 b$ and $b = 8$ .

$\frac{b}{(9 b + 8) (9 b - 8)} (72 b + 64)$

Step 4

Multiply $\frac{b}{(9 b + 8) (9 b - 8)}$ by $72 b + 64$ .

$\frac{b (72 b + 64)}{(9 b + 8) (9 b - 8)}$

Step 5

Factor $8$ out of $72 b + 64$ .

Tap for more steps...

Step 5.1

Factor $8$ out of $72 b$ .

$\frac{b (8 (9 b) + 64)}{(9 b + 8) (9 b - 8)}$

Step 5.2

Factor $8$ out of $64$ .

$\frac{b (8 (9 b) + 8 (8))}{(9 b + 8) (9 b - 8)}$

Step 5.3

Factor $8$ out of $8 (9 b) + 8 (8)$ .

$\frac{b (8 (9 b + 8))}{(9 b + 8) (9 b - 8)}$

$\frac{b \cdot 8 (9 b + 8)}{(9 b + 8) (9 b - 8)}$

Step 6

Cancel the common factor of $9 b + 8$ .

Tap for more steps...

Step 6.1

Cancel the common factor.

$\frac{b \cdot 8 (9 b + 8)}{(9 b + 8) (9 b - 8)}$

Step 6.2

Rewrite the expression.

$\frac{b \cdot 8}{9 b - 8}$

Step 7

Move $8$ to the left of $b$ .

$\frac{8 b}{9 b - 8}$